Right now british internet laws fall under the umbrella of European legislation so the answer is NO, however after Brexit and once the UK is out of EU Britain can make their own laws and do whatever they want and ban as many sites as they please. Will they do it?
I have no idea.
As Amy mentioned it's would be career suicide for american senators to not agree with the Sesta / Fosta laws as prostitution was and always has been illegal in the states so they can't condone something that is already against the law
Prostitution is not illegal in the uk
If it happens and I think it would be unlikely more likely to go down the Nordic Model first before anything else websites will probably just set up outside of the uk
Guys in the uk will use a VPN to access them
It's what happens in the Middle East and other places where advertising of sites are banned and sex is and prostitution is illegal
Wasn't there supposed to be some grand banning or age verification of porn site april this year
Whatever it was it hasent happend yet as far as I know