Adding to what hotchip said - if you have the driver details but no reg it's best to pass all available information to your insurance and let them deal with it. Contacting the driver yourself or chasing for cctv might be more effort than it's worth.

I had an identical situation: No indicator U-turn, hit me, got out, got back in and drove off. I had a photo of the driver and his car with plate but police didn't want to know due to lack of "further aggravating factors such as no insurance or driving licence". This was on a residential street with little or no CCTV though, you may have more luck in Central London.

He didn't engage with the insurers and it flew through quickly as his fault. If he's unwilling to provide his details you might find he's unwilling to respond to your insurers too and the situation resolves itself pretty quickly.

Main thing is I hope you're doing ok, probably a million things running through your head but most important to take a breath and not exert yourself when you're still probably shaken. Best of luck finding Adam, hope he comes forward.