It's not that "they're turning", it already happened. Tony Blair and Bill Clinton shared political platforms almost precisely.
A recent effort to go "back to their roots" (the Corbyn years) ended with a stalinesque purge of such leader. Sadly this leaves free reign for upstart neonazi and neonazi-adjacent parties (BNP, UKIP, Brexit Party/Reform UK...) to rip through traditional Lab heartlands.
> Tony Blair and Bill Clinton shared political platforms almost precisely.
I think this needs justification. There is no evidence that Clinton has ever been in favour of socialized healthcare for example, investment in which was a major tenet of the Blair platform.
They literally declared to belong to the same area, the "Third Way": https://en.wikipedia.org/wiki/Third_Way . They both loved Anthony Giddens' works, believed in triangulation and private-public partnerships as essential, morality-based foreign policy, etc etc.
On healthcare, the difference was due to the starting points in the two countries. What eventually turned into "Obamacare" was a push started under Clinton to address the obvious shortcomings of insurance-based healthcare in the US, providing an approximation of European universal-healthcare principles that could actually be applicable to the US context. Hillary Clinton was a massive supporter of that effort, effectively the link between the two Democratic presidencies. It just so happened that, because of the specific peculiarities of the US system (i.e. massive lobbying and astroturfing from insurance and healthcare giants), the actual law eventually morphed into what Obama enacted.
