I've never used a consultancy so not much help there I'm afraid.
There's a lot to be said for looking at what transferable skills you have - sites such as gradschools.ac.uk (which I hope works, it does) is aimed at phd students but has (at least did have!) a section on these skills.
If you've got a rough idea of what area you want to go into but not sure of what the job entails then it might be useful to contact someone specific at a company and ask for an hour of their time. It seems quite forward but the idea is not to ask them for a job but to find out what the job is like, good/bad points, how they got into it etc. A similar thing is work shadowing, where you follow someone round for a day or however long they'll have you for. Either way, it's a good way to build up contacts that could be useful if there's an unadvertised vacany.
Good luck anyway.