It's always dangerous to make generalisations about feminism, especially across different countries where the various splits evolved quite differently. The sex-positive version of feminism seems pretty dominant in the US but that's really not the case in the UK. The mainstream feminist voices you will hear in the UK media are almost exclusively not the sex-positive type that dominates in the US, other than a few younger writers. It's still very much dominated by what people call SWERF (sex worker exclusionary radical feminists) and TERF (trans exclusionary radical feminist) types of feminist. That's especially true of the liberal media like the Guardian and New Statesman. (Grassroots organisations aren't dominated in the same way as far as I can tell, and neither is academia, although I think you are still going to find far more 2nd wave type voices than in the US).
This stuff has been in the news fairly recently here because of an attempt by some feminist MPs to criminalise prostitution organised over the internet (and there are groups that have been pushing for it, some of them with links to the kind of evangelical US funds that you mention). There has been considerable backlash from sex workers and various grass roots feminist movements against this.
If you want an example a country where the sex industry has been regulated very differently then look at Norway and Sweden (if you start reading about this stuff you will quickly find people referring to the 'Nordic Model'). There's a huge amount of discussion of the topic academically and elsewhere. The results have not been what you are hoping for though (assuming your interest is reducing violence and exploitation).