Dean Street Express (the Soho clinic LL Punting is referring to) is the only NHS "same day results" service that I'm aware of in London, but increasingly difficult to get appointments for a check up without symptoms/proof of contact text I've found. 80 Leadenhall Street is another good NHS option , but also requires appointments and results are 2-5 days usually. Nowadays, I go for the postal kit option in most cases.
If I really want same day results, I'll go private with London Doctors Clinic who have branches all over town.