In the 'old' days, one had to use a qualified legal person (normally a solicitor) to advice one on property transfers.
In an effort to create a bit of competition, Government allowed the concept of licensed conveyancers. These are legally-qualified persons in property matters. They have to undertake training and maintain professional standards, and they are monitored by this outfit.
http://www.conveyancer.org.uk/about.asp
Look at the website and you will find a list of members.
You will very likely save money by using one of their members, compared to the charges made by a solicitor. Get an over-the-ohone quote for comparison.
I cannot explain why licensed conveyancers are not more widely promoted. The cynic in me says it is because there are too many MPs from the legal profession (vested interests).
In many cases if you go to a high street solicitor for this work, it will actually be undertaken by a junior (not fully-qualified person - but under the supervision of a qualified person).