I don't know a good place to get it cleaned, but I do know which place you might want to avoid. The dress alteration/cleaning shop in London Bridge station, the same level as the bus stop.
From personal experience, I had to get my wedding dress altered a few months ago there, and the ladies working there were quite dishonest, and tried to make a quick buck. Quoting me one price, and not writing it down, and then when I went back to collect the dress, they added extra money (I also went in before collection date, because I was worried, and asked to get the price quote in writing as they had promised, and was fended off by the owner saying she'll write down everything clearly when i come to collect). The handy work wasn't good either, having missed quite a few spots I requested them to sew. The owner was really argumentative, and even said to me: "You people spend thousands on wedding dresses, what difference does a few hundred more make!" Their view is, if it's a wedding dress, of course, everything will be more expensive, (although the service isn't high quality).
So, I just wouldn't trust it, despite it being a Wedding Dress shop.
My personal opinion only. If you are desperate and this is the only one in the neighbourhood, make sure you have everything in writing, including the price, what kind of cleaning you want, and what would happen if it is not cleaned properly.... all in writing!
best of luck!
(I ended up leaving the dress with my mum to clean back in Canada).
I had mine cleaned at Buckingham Dry Cleaners, 83 Duke Street, Mayfair W1K 5PF. Telephone number: 020 7499 1253
I did lots of research before choosing them, but the deciding factor was that my wedding dress maker recommended them, as they use them for their dresses in the showroom. It wasn't cheap, but wasn't that much more expensive than other dry cleaners who specialise in cleaning wedding dresses, and they did a fantastic job. And they cleaned my veil free of charge.
Due to daughter getting married next year, the only thing we seem to watch are wedding programmes...from bridezilla downwards..seeing scenes where the groom gets the cake and squishes it into brides face, my daughter said she would clout her groom if he did that, her hubby to be said it was a tradition..where I would like to know?
If you need to clean your wedding dress, never ever use SEW in Stanmore! I left there my wedding dress 2 weeks after the wedding , paid £125 and was told it will be ready in 2 wks. It was but in 2 months and to my horror , dress had new stains on it! I complaint but was ignored until my friend who knows in person that bloke Steven, phoned him up and complained about my wedding dress.It was ready within a week but still with stains on the train.I asked for the compensation but was told I won't get it as stains on the dress are old and they will never come off.Oh well.. I soaked dress in the hot water with washing powder and stains are gone with my money...
Do not use SEW if you want your dress to be cleaned and if you don't want to loose your money.