It depends how serious your injuries are - if it is a standard ' whiplash claim ' then you could contact the insurers of the other party and see if they are prepared to deal with you as a 'litigant in person '
If they are , they will inform you of the form and extent of evidence that they require .
Should you not feel confident enough to deal with the claim yourself or if your injuries are more serious , then there are a raft of claims handling firms out there who will be more than happy to take on your claim
A note of caution however - make sure you fully undestand the basis on which they will deal with your claim - ' No win no fee ' should be taken with a pinch of salt - read any agreement before you sign .
Incidentally , your claim, as the innocent party ( passenger ) will suceed against either one, of the insurer , of the drivers - i.e you can make your claim against whichever insurer you wish .