I used SAM Conveyancing which I found online and I'd strongly recommend them; their website is
www.samconveyancing.co.uk but you can call them on 020 7112 5388.
They quoted me a little over £600 at the start, which seemed good value to me, and they never added to this. This is the second time I've moved and what annoyed me last time was this whole bunch of hidden extras which the firm added during the conveyancing which nearly trebled the initial quote. I think I had to pay additional sums for silly things like photocopying.
When the seller caused a delay by not responding to some additional enquiries, my solicitor, a lovely lady called Shehani, really got stuck in. She was brilliant and kept me informed all the time and most of all, she spoke to me like a human and a pretty busy one! The whole process was over in about seven weeks.
So yes, I recommend these guys but I think, whatever you do, you should always go for a fixed fee quote. You won't get a sudden shock when the bill comes at a time when you're probably cash-strapped.