You will do just fine.
Billions of people past the driving test so why shouldnt you?
Ok, I failed my first driving test only because I showed up in a low rider and I was discriminated against. Had nothing to do with the way I was driving. I changed the car I used and went to a different DMV and passed with flying colors. Go figure.

I dont know what to tell you since I have never been to London nor have I ever driven sitting on the right side of my vehicle.
Keys are safety always first. Use signals always use mirrors and look back with your head and not always trust mirrors.
Good luck and drive safely