I don't think I'd call that Clintonite/Thatcherite. Thatcher was quite confrontational, and also hawkish socially conservative. Not dispositionally centrist, consensus oriented or antipolitical. Blaire is probably the PM you're looking for.
That "consensus" happened when the centre left accepted structural changes made by the previous "generation's" new right, Reagan & Thatcher. Economic issues became non-ideological, and technocratic rather than political from that point. This is even more of thing in the UK than the US, where the right wing still focused on economic conservatism rhetorically.
> I'm not disputing the US clinton part. I'm disputing the Thatcher part.
I wasn't disputing your dispute of the Thatcher part, I was disputing (in the US context) the center-left part.
> Blaire is "the center-right faction taking over the more left-leaning of the two major parties" and succeeding politically in the UK.
From my American perspective, it looked like that, but 1990s UK internal political party dynamics isn't something I’m nearly as confident of as their US parallels, so I wasn't going to take a stand on that.
That "consensus" happened when the centre left accepted structural changes made by the previous "generation's" new right, Reagan & Thatcher. Economic issues became non-ideological, and technocratic rather than political from that point. This is even more of thing in the UK than the US, where the right wing still focused on economic conservatism rhetorically.