Fly at night - you need a night rating. About 5 hours instruction...
Nationality - doesn't matter in the UK.
Location - I can't answer for London - I'm learning in Scotland - which is great but a bit of a commute...
Which plane to learn on - everyone has favourites but I wouldn't worry too much about which one unless you are very large. There are advantages and disadvantages of pretty much every plane going, but most people learn on PA28s or Cessna 152s. Nothing wrong with either of them. I'm learning in a SA Bulldog though - much nicer plane!