Many solicitors who specialise in divorce and family law offer a free half an hour initial consultation and I would suggest you make appointments with, say, 3 who offer this facility so that you can be advised as to your legal entitlements, discuss how long it may take before the divorce process is complete, what the eventual total cost may be, and whether you can apply for any proportion of the costs to be borne by the Respondent.
This will also give you opportunity to interview, as it were, your future solicitor as, particularly if it is expected that divorce proceedings may be protracted or contested, it is important that you find one that you have confidence in to kick arse move things along in a timely manner and in this respect it can be a false economy to make a decision as to who will represent you purely on price alone. As the saying has it, buy cheap and you may have to buy twice.
As you are in the capital city, you'll be spoilt for choice. Word of mouth recommendations can be the best way to source shit hot lawyers, or alteratively visit www.resolution.org.uk or ask on the Legal matters board stating whether you are north south, east, or west London.
Is there any particular reason why you anticipate that you will need a solicitor 'for a while'?