Natalia, assuming you are not looking to compete your PhD in the UK (at a UK university), I'm not sure what your best option will be. There are post-docs at UK universities though it depends upon what your subject area is as some fields are not going to have a lot. So a post-doc you'd do after you finished your PhD.
It may be possible to facilitate an exchange with a UK uni now while you are working on your PhD if for some reason there is something over here that could make or break your PhD.
Take a look at jobs.ac.uk - they post almost all the uni jobs and research positions in the UK though bear in mind this is a bad time of year to see what could really be available.
Also, unless you are a tenured professor over in the US be aware that the title 'professor' is only given to the most senior of teaching staff here in the UK. A lot of misunderstanding can arise if you tell them you are a professor when by their standards you are just a 'teacher' or 'lecturer' or 'reader'.
I'm doing PhD here in the UK, as is my husband (though he's English). Feel free to send me a PM (personal message) if you want to pick my brain at all!
Good luck!
(BTW, if you had the time and money, I don't think it would be illegal for you to come here for 6 months and spend most of your time at a research institution on a visitor's visa. You just absolutely cannot work and you'd probably have to prove you have the funds to last that long. I'm not certain of this but it might be worth investigating if all else fails.)