That depends on whether or not your CV will come across to the consultancy as someone they "absolutely must invite in for interview" or whether you are someone who would make a great hire for them but that they might pass over during the CV reviewing stage...
A recruitment consultant putting you forward gives some added credibility to your application - it means that someone has vetted you as an applicant and is prepared to put their neck on the line with their client and tell them that you are worth interviewing. This isn't done lightly - you'll only be put forward to a client if the recruiter thinks you will impress. So if you aren't an obvious candidate for a role on paper - but do actually have the skills needed to do the job - then a recruitment consultant can get you that foot in the door that you need.
Against this you must set the (employer's) cost of using a recruitment consultant, which is going to add £15,000 to the cost of an average hire - so clearly a consultancy will have a preference to take someone who has applied direct vs. someone that has come through an agency.
If you are a McKinsey consultant trying to get into a small strategy boutique, you probably don't need a recruitment agent representing you to achieve this; if, however, you are a consultant at a small unknown strategy boutique who wants to get noticed by McKinsey, then having a recruitment consultant put you forward might just achieve that.
Hope that helps with your dilemma!