you could try contacting the guildhall school of music in the barbican which is near se1, you could use one of their teachers or a student, depending what level you are.
i think that you can also take lessons at morley college too.
I'll second that message, I've wanted a piano for years too. It has to be smallish as well, to get round the corner in the stairwell. Come to think of it, anyone know of any decent (and, goes without saying, reasonably-priced) piano movers? What might you expect to pay for delivery including one flight of stairs?
Much lighter, much smaller, much more flexible, able to be used with headphones, can do different sounds and be used for fancy digital stuff - yes I have considered a digital piano, indeed I've (sort of) got one. But its just NOT a piano. Anyone who grew up playing the piano will know exactly what I mean. I just lust after a real piano. Nothing else is the same. A grand in the bay window of a big room is an unattainable dream. But a battered victorian specimen in the corner of my flat will do for the time being.
For both pianos and piano movers, try Marksons (based at Woolwich) - 020 8854 4517. Also have a look at www.uk-piano.org.
I found Marksons through my work - musical event management. They use a specialist piano moving company and they have moved my Broadwood upright twice, including round rather difficult stair ends etc! Also, my old flat-mate (a singer) bought a pretty good 2nd hand piano from them last year and is very pleased with it - I think it was about £1000.