You're certainly entitled to make a civil claim against the van driver. Details of the the court procedures are here:
http://www.hmcourts-service.gov.uk/infoabout/c laims/index.htm
However, no court will consider a claim unless you've given the other person reasonable time to pay. i.e. you can't go straight to court; you've got to send the van driver the bill for your repairs first. It's only when he fails to pay up that you can take court action.
You should also remember that someone driving their vehicle into yours does
not give you an automatic right to claim compensation from them (or from their insurers). You must be able to show (based upon the 'balance of probabilities') that the driver was
negligent. If, for example, the van driver had swerved to avoid a drunk pedestrian (or a dog), you'd have no right to claim against the driver. (Any claim would have to be made against the drunk or the dog owner in order to be successful). The van driver might say: "Yes, I did hit the other two vehicles but only because a drunk stepped into my path". If the court believed him (or, at least, thought that his explanation of the circumstances was more likely than yours) your claim would fail.
Chris