If problems arise, it helps if you can talk directly to the person doing the conveyancing. Your signature will be required on a few documents, so it's also easiest if you can just call into the office to deal with it.
Personally, I'd prefer to find somebody locally. The problem is, though, that many small firms have been bought out by solicitors. I've just taken a look under 'Conveyancers' in my local Yellow Pages and I can only find one firm which isn't actually a solicitors' company. Even so, that would be the firm I would contact first before trying the solicitors. (If I couldn't find an independent licensed conveyancer, I'd ring round all of the solicitors offering 'fixed fees' and get the best quote).
Chris