@EB1Aspirant When I received the IL from NVC, it stated that my case was moved to London embassy, if I want to make any changes, I have to contact the embassy, which indicated that NVC has no longer worked with my case since then.
Now your case is with London embassy, so, if the embassy haven't arranged an interview date for you, I think you need to book it by yourself. The best way is to contact the embassy directly for further support.
But before that, make sure you arrange a Visa Medicals health check.
Hope you can sort it quickly. Good luck.