If the mediator charges £200 per hour that is half of what it will cost you both for solicitors, the real saving comes because the mediator if all goes well will tie it all up in 4-6 hours, so will luck it would cost you both around £1000 all you need then is a Consent Order which from wiki costs £139.
If you compare that with what it will cost for you to both engage solicitors its a fraction of the cost.
Most mediators like face to face but some use skype, one answers questions on wiki, his name is imediate, maybe you could message him, he may know a mediator local or be able to help himself.
First of all, I am afraid I don''t know a mediator in your area. Your local Citizens Advice Bureau might be able to help. However, I have just googled and found there is Birmingham District Family mediation (bdfm.org.uk). I know nothing about them but they may be OK.
Dukey has kindly mentioned me as I am a mediator and have written an article on the subject and has a link to it in the mediation section of the forum. I have to be careful about promoting my business in this area of Wikivorce but, if you wish to do so, you can track me through my details on this site.
All I will say here is that I am qualified as a boring chartered accountant and I mediate with an ex-family law barrister and you get the two of us for less than the price you were quoted! And we do do work over Skype which, whilst not absolutely ideal, does seem to work surprisingly well.