Undergrad - a few points I'd throw out here:
1. You don't share your university credentials - where you're studying and what grades you've obtained to date. These are absolutely crucial details for securing a job in consulting and if they're not in the league that firms would be seeking then no amount of extra-curricular point scoring is going to overcome that.
2. I would argue that work experience is not valued so much for what you learn during the work experience but i) because it provides a degree of reassurance about your candidacy ("he/she got an internship with Deutsche Bank so they must be pretty good") and ii) because it shows a degree of get up and go / ambition / drive from the candidate. Internships give you exposure to working life but experience-wise they don't give you any meaningful headstart over candidates without work experience that a good employer wouldn't have eradicated in your first weeks on the job. Of course they do also give you a foot in the door with a potential employer, which is another reason why an internship with a major employer is a lot more worthwhile than one with a minnow.
3. Correspondingly, anything you do during a gap year needs to tick the boxes of providing reassurance / credibility and / or demonstrating ambition / get up and go (if you want the gap year to assist in securing subsequent employment). Experience gained with smaller firms is unlikely to impress mainstream employers in the same way that having secured an internship with a major brand would do. By contrast having the get-up-and-go to spend a year abroad learning a new language and / or working in a new culture will be a far stronger differentiator - so if you're going to do unpaid work at least do it somewhere that sets the pulse racing, is character-building and will be a talking point.
4. For regular internships you could check http://www.ratemyplacement.co.uk as a lot of the major brands advertise their openings on this site ; if you're not getting anywhere with mainstream internships (or indeed even if you are) I would personally recommend taking a look at the Southwestern programme (http://www.southwestern.com) as a great way of getting strong sales skills onto your CV and also improving your ability to sell yourself. I and many friends did this and I can certainly vouch that it opens a lot of doors and impresses on a graduate's CV.
Hope this helps and good luck