this should be a good place to start:
http://www.managementconsultancy.co.uk/webdirectory/mctable
in terms of advisorys well it depends on the sector of central govt - you could argue pretty much everyone. be more specific is it
transport,
strategy,
operations,
programme management
the list goes on and on. and so do the firms.
have a look at the tables in the link provided and go to each company's website to see what they do.
best of luck
cheers