I second a chat with Cats Protection and independent, no kill rescue. Ask if they have a trap to loan you. If all else fails please pm me and I will put a call out to rescue contacts to see if someone local can supply one.
Equally your Dog Warden, whose real job is Animal Warden, may have a trap, IF your council has one and has not cut costs by just having a stray dog seizer as demanded by law.
As someone who works with independent rescues I couldn't agree more that the RSPCA are a profiteering nonsense who are unlikely to help, sadly.
Re a trap, bait with smelly food - pilchards work well, the canned ones in tomato sauce, NOT in brine, and which you should rinse clear of sauce first.
You CAN construct a trap yourself using a cat basket or dog crate and attaching a string to it, ready to pull down as soon as the cat is inside (done this!) but of course it means you have to be there indoors, hand on the string, when the cat walks into the cage.