Can anyone tell me the best public sector consultancy firms and what sort of backgrounds they look at?

Biggest ones that specialise in this are Capita and Hedra. Both pretty good, as far as I know.

Capita, Hedra? Biggest public sector consultancies? Absolute rubbish. Capita are an IT implementer, nothing more, who weekly tarnish their corporate reputation through screwing up UK government contracts. Hedra are indeed a Public sector consultancy, but are small, at the lower end of the price range and so do not make half the margins of the big players. Neither are great to work for, according to those who are really in the know. Who aren't bottom feeders? PA, Deloitte, PwC Performance Improvement Consulting, Accenture's new strat group, Atos, CGEY, Detica, McKinsey. These are the biggest players with the premium reputations in the market. A breakdown of all these firms are available on this site. Hedra? Capita?? I think I need a lie down......

PA do a lot of public sector work: mainly for local authorities, and the likes of the Met and TfL. They look at all types of backgrounds. Good luck with your job hunt !!