When it comes to protecting your anonymity, I'd suggest remembering that you are a face in a very very large crowd. You may think you are a special and unique flower, but you are just a guy that punts. There is very little reason why anyone would spend time tracing you, over the thousands of other people that punt every hour.
It's a legal activity, you are not buying guns/drugs.
By all means, take sensible precautions. Don't imagine that it makes you an elusive Jason Bourne type, flitting in between the shadows of society, you're still you. It's possible to track you, trace you if you have the equipment knowhow and time, but (and this is important) nobody fucking cares and the girls you are visiting are not elite Russian trained counter agents.
Unless, of course, you work for GCHQ. In which case, you boss is probably reading this and pissing himself.