Do some research for yourself on companies like Accenture, CapGemini, IBM and their recruitment routes. It might be a bit difficult as you don't fit into either the grad scheme or the experienced hire bracket, but you could try and make an argument for either. If you're an impressive enough candidate, anything's possible.
If you're really really serious about 100% wanting to switch to consulting and nothing else will do, you could try and do an MBA. That would certainly up your appeal as an experienced hire, and when you add your 10 years of technical experience (albeit with non-transferable knowledge, but surely with transferable skills), you might* be quite likely to get in with one of the above tech-based consultancies, and from there you could gradually try to move in the direction you want within the sector.
*I stress the might here because I don't want you to go and do an MBA cos you think I told you you could then be a consultant. There are a whole range of soft skills that consultants require that you might lack for all I know, so no amount of extra qualifications etc. would get you in.