The home test kits are just as good as what you get in a nhs clinic. They use the same test equipment, just done in a private lab, usually Doctors laboratory in London which is a very highly regarded test centre and where all the London clinics send their samples.
With regards the tests, the combined urine testate for gon and chlamydia are fine. Piss in a pot firest thing in the morning, pop it in post, results within 2 days.
Hiv test - the oral swob ones are not very good in terms of accuracy. The blood ones are better which test after 28 days by detecting antibodies or p24 antigen.
Have look at better2know website as their prices are pretty good for home tests.
However..... what you don't get in a home test kit is the professional advice, free service, or treatment if something is detected. Plus, many nhs clinics have small laboratories within and can take a swob and tell there and then if you have a bacterial infection.
So it's up to you. I've used home test kits in the past and had no problems provided you follow the instructions.