Theoretically neither of you needs to instruct a solicitor. (It's possible to do everything without one). But it would probably be best to use the services of a solicitor or (even better if you can find one) a licensed conveyancer.
It's also possible to save on costs by using the same solicitor. He/she would be allowed to act for both parties as long as no conflicts of interest were likely to arise. (I sold part of my garden to my next door neighbour, using the same solicitor to act for both of us).
The (last) Government had originally planned to make it essential to obtain a Home Improvement Pack when selling your home. That proposal was scrapped (as of last May) but a small part of the legislation remains in place; you'll need an Energy Performance Certificate:
http://www.direct.gov...ertificates/DG_177137
I've only ever sold two houses but I didn't use an estate agent in either case. As far as I can recall, your solicitor(s) and/or licensed conveyancer(s) should do everything that is necessary (apart from obtaining the EPC, as above).
Chris