To me this is a simple service transaction - they check the land title, establish the contract for the sale, deal with the monies, then deal with the Land Registry to record the new title. With the use of the internet to exchange information between client and customer, there's no reason why any face to face is necessary. The contract for the sale / purchase has to be signed / witnessed, but that can be done by post.
Far better therefore to save money and select your conveyancer according to price. Every professional operating in this market has to possess professional indemnity insurance to operate. This means that in the unlikely event that things go wrong because a mistake is made, there is the insurance back-up to sort it.
If one asks a range of solicitors across different parts of the country - from SE, South Wales, the North, for a verbal quote, they will all come out within a very narrow range of price. This may be possible if the Law Society produces a indicative scale of fees based on the transaction value - solicitors probably follow the scales closely.
However you are very likely to find a lower scale of costs using a licensed conveyancer. More is explained here.
http://www.conveyancer.org.uk/about.asp