I am curious to see solid historical answers to this question, but I want to add some caveat/context to the question. The separation UK/EU vs Aus/USA is hardly that clear cut if you look at economic data.

As a proxy, the total government spending as percentage of GDP in OECD countries can be seen here:

https://data.oecd.org/gga/general-government-spending.htm

Roughly this number tells us how much of the spending is democratically/collectively controlled vs individually controlled.

The USA and Australia at 37.2 and 36.4 percent are indeed close together. But France (56.7) is more different to Germany (43.9) and the UK (42.4) than they are to USA/Australia.

If you only focus on the social protection spending category of the OECD, the USA and to a lesser degree Australia move further down the spending ladder, but they still very much exist in a continuum with the European states.

So at least some of these cultural naratives do not reflect facts on the ground in a staightforward manner.

Edit: The UK only closed the spending gap to Germany during the Blair Government in the late 90s, early 2000s. 1996, the Year before Blair takes power, the UK is at 35.8, the US at 35.4 while Germany is at 48.9 (just down from post reunification highs), much closer to Frances 54.6.

So for the sake of sticking to the 20 year rule, the question should maybe put the UK in the USA/Australia basket:

https://data.oecd.org/chart/5awn

From this perspective the end of the 20th century looks like Anglosphere vs Continental Europe as far as the Western world is concerned, with both having members that are on very different trajectories.

I'm not sure this is accurate - Australia's welfare network is more similar to the UK than the US (e.g. we have socialised healthcare and our loans system for higher education is far less of a burden). And then both the UK and Australia are quite different from the Scandinavian social democracies.

Are you asking about the development of cultural attitudes towards social welfare or why welfare programs exist as they do today in the UK and in Europe?

I would like to follow up with: Is there a historical connection between having a parliamentary system and the strength of the labor movement within a given nation?