In reply to Mr Goose:
If you work through a gallery then they can manage stone-shipping for you. My engagement ring came from this woman:
http://www.nataliejaneharris.com/ She's based in Nottingham, and the ring of hers that I chose at
http://www.kathlibbertjewellery.co.uk/ in Saltaire had to be completely rebuilt due to my galumphing great hands and the scarcity of the stone in it. The gallery sorted out all the to-ing and fro-ing, and because they're experienced (and deal with independent jewellers) they sorted out all the measuring, etc.
If you can't find the right jeweller in London, then perhaps finding someone who acts as agent for some independents might be the way forward.
Oh, and Natalie also works with existing stones. She's a lovely woman!