what specific conditions would I need to grow tea in London and how far apart should the plants be?

This is totally the wrong climate for tea - otherwise we would all be growing it!!

would it not be possible at all to grow it in a greenhouse?

Not unless you can afford to keep it at the sort of temperatures Wisley or Kew can.
Cost would be greater than the product is worth. You also fo not get that much leaf from one shrub either.

There is a garden in Cornwall that is now growing tea. But I think that you would have to have a lot of plants to be self sufficient. How about some mint instead for mint tea?

hydroponics wood work well but cost you deer as other people have said

Even if you can get the tea to grow you would then have to process it which would not be cost effective for a few bushes.