As I have pointed out a common opposition to a concept of "privilege" bound together the liberals. AT the same time both their support base and their policies were very varied. This was true of virtually all major national issues of the day-free trade being the great exception and to a lesser extent Home Rule and weakening of the House of Lord’s power. On just about any other issue you could fine two liberals with opposing views- and it is my impression that while there was also considerable diversity in the Conservative/ Unionists.
Nor were the liberals necessarily divided into clear factions in this period. They were at their most divided in the early 1900's when a powerful faction was strongly opposed to the Boer war -indeed at least in the latter stages a majority one! Another powerful faction (almost certainly representing majority opinion among the electorate as a whole) supported it. However there were general tendencies and I will now try to describe what I see as the three most important (using my own categorization though based on ones used at the time and by historians).s. It should be noted that there were combinations between them and subtleties in the spectrum within them-these categories are very general. So the Liberal Imperialists for example including those who were gung ho on imperialism and quite tepid on bits of social reform like Rosebery.
The first I would call "Gladstonian"- the straight continuers of the Gladstonian legacy. In a sense they tended to stand for an extension of his reforms ( Gladstone himself was dubious about quite a lot of these extensions such as women's suffrage) -and were perhaps the purest opponents of "privilege" in the sense of distinction They wanted to extend the franchise enthusiastically, introduce Home Rule (in many cases for Wales and Scotland as well as Ireland), and take Gladstone's sympathy for national movements and opposition to further levels- they were often outright opposed to the imperial and provided a big base for anti Boer War Feeling (and indeed for anti First World War sentiment to a lesser extent) . Similarly they were very wary of higher defence spending or foreign intervention. Like Gladstone's governments they were often sympathetic to crackdowns on "vice"- for example alcohol and prostitution unlike most forms of government such policies did not make distinctions between people in a privileged way. And John Stuart Mill was never the liberal party’s mainstream. However they tended to be more sceptical of the politics of social reform-which provided distinctions-attacking it as encouraging dependency and as a new form of privilege. John Morley was the major member of the Asquith government most opposed to the new social reforms- and the world of 20th century statism from pensions to labour regulation to growing regulation of private industry.
This may make the Gladstonians sound like a mere relic- a continuation of the politics of the past. However they were still a vital force within their party including I would argue such dignitaries as Millicent Fawcett who was both fanatically committed to female suffrage(even being willing to support Labour for that reason) and an opponent of old age pensions!
The best election of the era for the liberals was 1906-an election fought on the pure Gladstonian issue of free trade and to a lesser extent other principles like non-denominational education and opposition to "Chinese labour" that fit in well with Gladstonianism. Secondly in a sense they were actually the most resilient liberals. The tiny liberal party that survived into the early 1950's was much closer to Gladstonians than either of the other two tendencies I will describe-strongly supportive of internationalism and "peace movements" but very free market and anti-socialist (indeed such describes quite well Joseph Grimond who started their revival).Founders of the revival of free market thought in the late 20th century were often members of the liberal party of that era for example Arthur Seldon. It's worth noting Josiah Wedgwood who at least in the latter party of his career was a pretty pure Gladstonian even joined the Labour party!
Another group I would label the "radicals" or the "advanced" liberals. They tended to share most of the Gladstonian style objectives. At the same time they combined this with a new agenda attacking different forms of privilege. For example the "privilege" of land ownership ( Georgism was strong in the liberal party as was ), inheritance and profits that were perceived as being the result of monopolies. Hobsonian positive liberalism with its scathing attitude to capitalism and imperialism was very much part of this tradition . This section of the party tended to be the most enthusiastically anti drink -lacking the free market scruples of many Gladstoninans. Unsurprisingly in the inter war years many of this group ended up in the Labour party whether Addison or William Wedgwood Benn. Indeed in many ways it can be seen as perhaps the foremost ancestor of the middle class leftwing tradition within the Labour party. Lloyd George before World War one(World War one had a big impact on hams!) Was perhaps a classic example of the way in which radicals combined the old liberalism and the new- anti-imperialist, with strong pacifist tendencies (without quite being pacifist), anti establishment, pro Welsh nationalist (and crypto prohibitionist)- and the leading architect of the social reforms that lay the foundation of the Welfare state.
I would argue this wing (even on alcohol) had marked resembling to the populist and progressive wing of the Democratic Party in the United States. Even those Democrats enthusiasm for the "autonomy" of southern whites was matched by similar sentiment among liberals about the autonomy of Afrikaners in South Africa. And there is an even more direct parallel in that southern progressives were very critical of Theodore Roosevelt’s effective support of the UK in the South African War (as to be fair were most Americans with a view).
There was at least one other faction in the party in the decades before the World War I> The very powerful liberal imperialist wing (which included at a minimum the second most important liberal prime minister Herbert Asquith) which strongly backed the Boer war and the maintenance and even expansion of the empire-helping split the liberal party They were chiefly responsible under Asquith and Grey (his foreign secretary) for the embracing of an increasing tight alliance with the French against Germany and for a large increase in defence spending to guarantee British naval superiority- in a sense a foreign policy that much more naturally. I think it'd be fair to say they had less archetypical liberal" background-they were often aristocratic or semi aristocratic, Anglican rather than dissenting and so forth-at least in parliament (though so overrepresented were these groups in parliament they were large in all three factions) . This was often reflected on what might be called socio-cultural issues drink and suffrage where I would estimate they tended to be less sympathetic to the "reform" position of restriction and enfranchisement than the average Liberal- Asquith and Churchill opposed women suffrage and alcohol restriction as well as being notorious drinkers!
So why were they liberals -were they just a historical accident people in the wrong party? As already mentioned though this was an era where party voting was getting tighter not less. The Whigs who much more plausibly could be seen as "being in the wrong party" by the late 1870's (where the reforms they battled for had been implemented or negated) had already defected. I would suggest several ways in which the liberal imperialists were natural fits with the liberals-indeed not sparingly since so many of their most distinguished leaders fit this profile!
Firstly they may have been imperialists but still had important differences with the conservatives- they often had a more "pluralistic" conception of how empire should work usurping they accepted (and mostly supported albeit in a way cautious of the electorate) Home Rule for Ireland. Its worth noting Cecil Rhodes was almost certainly a liberal imperialist-even giving a large donation to party funds. Cecil Rhodes in pandered to Dutch Reformed hardliners in South African politics- Liberal Imperialism was not by and large simply a copy oft hat of Joe Chamberlain. Rather it looked to a looser empire where cultural pluralism could find political expression in Home Rule , enormous automaton for members including Dominion status for a Union of South Africa with an Afrikaner general (and headed by a man who had been a general against the Births a decade before) and without tariffs. It was a less cohesive . Consolidated and centralized vision of empire.
Secondly they tended to be very sympathetic to social reform-there was a section of Conservative imperialists for example Milner who were also sympthatetic to social reform-but the liberals were the party that pushed it. In many ways that fit in with Social Darwinian ideas that underlay much of the imperialist vision-and the notion of using government to strengthen the nation. At the same time many of the arguments on the "social surplus" or the dangerous effects of unregulated capitalism were accepted by many liberal imperialists. A supreme example was Grey in this period who has been aptly described as part Whig and part Socialist - his embrace of Tory polices abroad was matched by an intense support of state regulation and control at home- representing a common vision of improvement and diversity through government ( he grew disillusioned with state control due to his experience in World War I. An even better example was Haldane -regarded as being on the extreme right of the liberals during the Boer war -but who after World War I happily served in a Labour Cabinet! In a certain sense they can be seen as the most "modern" of the factions- committed to both the great trendy causes of imperialism and domestic welfare.
Lastly of course much of the constitutional agenda was supported by and large by the imperialists. It's worth remembering that the greatest issues of the era were probably the House of Lords and Home Rule-the latter of which led the UK to the brink of civil war. Asquith was as keen supporter of both as the "radical" Lloyd George.
Many liberal leaders were prominent liberal imperalists.The (relatively) young Churchill was arguably a classic one- a former Tory who'd left over free trade, a war veteran, an aristocrat, a hater of female suffrage and alcohol, a believer in a relatively strong defence, a social Darwinist-and a massive supporter of social reform much more so than the likes of Morley. But their supreme leader and perhaps an even purer example of the breed (Churchill arguably had radical tendencies) was Herbert Asquith the enormously powerful Prime Minister from 1908 onwards whose countenance heads this post.