Looking at the political landscape, it does appear that the United States is moving to moral liberalism, whereas Britain seems to be getting increasingly conservative. I can't really speak for our economic direction yet, since it seems like our own politicians have no idea what they are doing, let alone myself or any other observer.
if anything, I think the US and the UK are converging. The Democratic Party platform doesn't contain much at all the Conservatives would object to; the Democrats are marginally to the left of the Conservatives but I don't think the difference is especially significant. George Osborne already raised the living wage (to the equivalent of $10USD, but I would not be surprised if May increased it again as a coup de grace). The minimum wage is already indexed in the UK and the Conservatives do not oppose it.
The Conservatives don't typically support pro-union reforms, but all the union reforms mentioned in this year's Democratic manifesto are already standard law in the UK; there's no need to abolish "right to work" laws because they don't exist; similarly there is no forced arbitration.
The Conservatives already guarantee more paid leave after maternity than the Democrats actually offer, the same amount of sick leave.
You can go through the whole Democratic manifesto like this. The only things I could find in the Democratic manifesto that I think enough Conservatives would oppose to stop being law/not become law in the UK are:
Privatizing the UK postal service (which they already did)
Credit agency reforms
Millionaire surtax
Decriminalization of marijuana
Free community college (although Clinton's plan rather than the Dem platform specifically is very similar to the UK's current system, implemented by the Conservatives, so maybe not even this)
There's also a number of things even the UK Conservatives are in favour of that are politically non-viable in America - the NHS, for example (I mean, the Conservatives want to privatize parts of it, but making it a public insurance option is beyond all but the nuttiest of them).
So I don't think America is turning into some sort of liberal democracy or the UK into some moralistic hellhole; I think that broadly speaking, all Western countries are beginning to converge in terms of their political infrastructure and outlook as globalization ensures they look ever more similar and so call for ever more similar solutions.