I don't think you can weld 501, just braze it.
Mercian in Derby will fit a whole new seat stay for £55.00 but I would guess they could do it simpler and cheaper than that, however. Talk to them. If they put a new seat stay on it it'll be better than new.
Of course they're a LONG way from you and I don't know how much shipping would be but I bet they could recommend someone in London.
http://www.merciancycles.com/renovation.asp