There is no law that you need a solicitor to transfer land in England.
[ like there is a law that says the transfer must be written and not oral ]
The estate agent is probably employing a licensed conveyancer ( law bod that only does land transfer ) and I use them a lot - I find the service good. Others of course ( as they would say with solicitors or barristers ) have had less wonderful service
I wouldnt use anyone 'lower' than a licensed conveyancer - like the estate agents wife who does a bit on the side - or mrs slopp up the road - or even yourself ( but people have done all these things ) as that is more prone to future issues
Agree with PP, but do not assume estate agents licensed conveyancer will be cheaper. Know of a case in the last month where estate agent has quoted £595 as the raw fee, whereas by phoning around the equivalent service was got for £295.