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I'm not sure how far east they go but I used Dan James http://www.danjamesconstruction.com/ for mine. Mine was a bog standard conversion in a victoran terrace with no special requirements.
I was in general very happy with them and would use them again. Had some issues with the architect who I didn't particularly rate but it's possible I wasn't clear enough and they were sorted easily enough.
However, I know that @brokenbetty didn't have as smooth an experience with them although I think hers was a bit more complicated than mine.
I heard some worrying tales about Simply Lofts when I was looking so didn't bother with them.
I also got a quote from this guy http://www.loft-conversion-specialist.co.uk/ Has a decent reputation in the area but didn't use them so can't personally comment.
EDIT: I'd spend a bit of time on your council planning website seeing what did and didn't get approved, get an idea of possible size, inspiration for plans, etc. I found that very useful
Am not having much luck using the search, although I know there have been many conversations about the following: I am looking for recommendations for loft conversion in London (East) We're in a Victorian terrace. I am planning to knock on a few doors locally, but thought I might try here first. I am already in contact with Absolute Lofts and Simply Lofts, so would be interested to hear of any experiences with them . Thanks so much.