My advice would be to send your CV to the major consulting firms direct. Many of them have graduate recruitment schemes and if you have no experience at all this will be your best route in.
Alternatively you can try some of the recruitment agencies - much of the market is controlled by agencies in the UK. Which agencies you try will be dependent upon what type of consulting you want to enter into. However, they generally want proven experience.
Bear in mind during your search that the consulting market is just starting to pick up and competition for positions is very fierce. You may also find that UK personnel do not understand your qualifications and you will have to learn to describe them in the UK equivalent. You will also have to deal with the visa issue if you do not have dual nationality.
If you do not get in this way, then look for an interesting position in industry, and apply to the consulting firms again with 2 years work experience in the UK under your belt.
I have been down this route myself - I moved to the UK 5 years ago, after completing my Honours degree, went into industry for 2 years and then made the move into consulting.