You can find the website of the Law Society's Legal Complaints Service here. It explains the complaints process well, in simple terms. The board is made up of 7 solicitors and 7 lay people (listed here). It claims to be independent from the Law Society but is part of it. See if you can find some statistics about how they are doing now - are things any better than in 1996, when a frankly appalling 2 out of 3 complainants were unhappy about how their complaint had been dealt with? No wonder they've rebranded the service so often - first it was called the Consumer Complaints Service (CCS), then the Office for Supervision of Solicitors (OSS), and now the LCS. But can a leopard change its spots? In 2005-6, only 66% of complaints were dealt with satisfactorily. Still not great.
For Barristers it's the Bar Standards Board that deals with complaints. They claim to be independent but are part of the Bar Council and are a mix of 8 barristers and 7 lay people, including the chair. By contrast with the LCS, the BSB handle 90% of complaints satisfactorily. Much more like it.
Given the generally poor record of the legal professions in dealing with complaints themselves, it's hardly surprising that the government have created various ways of keeping an eye on them.
Zahida Manzoor CBE (below) is the key figure here and wears two hats: she is the Legal Services Ombudsman and also the Legal Services Complaints Commissioner. She's not a lawyer!
Her powers as Commissioner under the Access to Justice Act 1999 are set out here; basically she can set targets for the Law Society in respect of complaints handling and fine them if they don't come up to scratch. In 2006 she did just that, fining them a whopping £250,000. That'll learn 'em. She doesn't oversee the Bar Standards Board though; that's done by another independent Lay Complaints Commissioner with much less power - presumably as the BSB is less of a problem (you can read their 2007 report here).
If a client is unhappy with how a specific case has been dealt with by either of the above bodies they can take that case to Ms Manzoor in her capacity as the Legal Services Ombudsman. She can force the solicitor or the Law Society itself to compensate the client. Bet they don't like her very much!