if a centrist in the UK would be halfway between current Labour and Conservative policies, that would probably make you close to a mainstream Democrat. Labour is left of the Democrats and the Conservatives are right of them (primarily economically), but neither by a huge margin.

I agree with you. I would go so far as to say that the Conservatives are to the left of the Democrats, even economically. Look at the extent of public borrowing funding all the furlough schemes etc. Not to mention both Labour and Tories are fully behind free public healthcare, which Democrats are having to be dragged kicking and screaming towards. Although that is rather a special case.

Come to think of it I can't think of any policies on which the (mainstream) Democrats are to the left of the Conservatives, but maybe I'm not thinking hard enough.

That's a good point, especially since Thatcher the conservatives haven't even been all that economically right wing. They do have a tendency to cut public sector spending, with austerity and such policies, but the UK starting point for the welfare state is much more than the US.

And if you move one inch to the right, you will be branded a right wing fascist. It has become extremely difficult to be seen as part of the center.