Neo unless you know someone with a code reader, I would think the cost of a secondhand transponder from the breakers would weigh far less than to get a code read. Also the basic code readers may not all have the same specific capacity as dealership equipment to give you a pin point code.
I would contact the a decent breakers like Charltons and get a UK spec 2nd hand transponder for the rear right wheel arch and see how you get on.
If the problem persist after changing the transponder, then take it straight to the dealers or an independent garage with appropriate equipment for further investigation. The dealers use Starscan to interrogate the system and charge something like ~ £90 per hour for a diagnostic, so it can be expensive.
Good luck, hope it gets sorted