Just wanted to say that you don't need to use a London based divorce lawyer even if you live in London and it is much more expensive if you do. You might want to see them once at the start, but even that can probably be done over the phone and even if you do visit them once it will still be cheaper than using a London lawyer.
I'm an ex lawyer (not divorce law) and I chose to use a divorce lawyer from outside London for that very reason. My XH has been through two leading London divorce firms and TBH they have been nothing special.
Personally I would want someone who is on the advanced (not just ordinary) family law solicitors panel and who is a member of Resolution and a trained mediator (because they approach things in a different way). You can search and find someone who is on the advanced panel by area on the Law Society website. Then google them and check the Resolution and mediation points.
If you believe the legal directories have it right and you really want a first or second tier firm in London then look at the entries in Chambers and Partners for top family law firms at www.chambersandpartners.com/11814/27/Editorial/1/1 or their equivalent in the Legal 500. Once you have decided on the firm you can re-search by individual within that firm and decide who has the best profile for your needs. All these firms are big money though and there are many good lawyers outside London.
All divorce is expensive as soon as you involve lawyers. But definitely don't make any concessions on children or finances without a full briefing from your lawyer on where you can expect to come out in your personal circumstances.
Top tip: if your STBXH is the one with the money, now there is no legal aid in divorce, ask your lawyer about getting to decree nisi as quickly as possible even if nothing else is agreed in order to get the court to make an order that he pays your legal costs.
Good luck!