Prostitution in the UK - is it lawful?

I know it's not illegal (although various related activities are) but is it lawful?

Memory is telling me it isn't: thus you can't enforce a contract based on sex in the courts, just as you can't enforce a gambling debt.

The case I remember involved a woman who agreed to part-pay for a car through having sex with the seller a number of times. When she stopped having sex with him before then, he sued to get the car back for breach of contract and lost (and if anyone has a reference for that case, I'd be grateful!)

Memory is also telling me homosexual acts aren't 'lawful' either, merely decriminalised...

Another question for people with access to a online legal service

I've found the law reports plus speeches for a number of cases, including Shaw v DPP (1961) (publisher of prostitutes' ads convicted), R v Knuller (1972) (publisher of gay personal ads convicted) and R v Brown (1993) (the Spanner case).

What I'd love to have is the same for the post-Spanner case where a married couple were acquitted of assault, despite having done more damage to each other than the Spanner men...