Variation is mainly influenced by the sector/function you consult in, more than by individual firm culture. Although high travel and client-site working is still the norm in U.S. and in some I.T. consulting, many firms in London will have you based in or near to the office 50%+ of the time because most clients are so close at hand.
In terms of consulting firms favouring medics, there are opportunities in healthcare and "pharmaceutical" practices within many larger consultancy firms (Deloitte, Accenture, IBM, PA, etc.). Mainly projects cover NHS and DH consulting. However, for your medical qualifications to give you an advantage in consulting, you'd normally need some experience as well. Otherwise, you could always apply as a standard graduate and specialise later.
Atos Origin have been specifically recruiting recent medical graduates for their medical services practice recently and may still be doing so.