You can easily get the right lights in the UK. Arcadia 12%UVB tube is what you want. Other brands can be less effective. A choice of round basking bulbs for heat and light are readily available.
So yeah, the UVB tube is what matters most right now. Make a note of tge date as a UVB tube needs replacing every 6 months.
It sounds like he is feeling better!
As suggested, UVB lighting & heating make all of the difference in the world for them. Since you are in the UK the Arcadias are or should be easy to find. The tube bulbs are top of the line.
I am sure he loves having a little cover over him too, your tank top.
A lot of them prefer to go potty in their bath which is convenient though & keeps their tanks clean, too.
That's too bad the family before didn't want him, how sad. I'm glad you are giving him a great home now!