It's a criminal offence to sell an unroadworthy vehicle (except under circumstances which clearly don't apply here).
If you suffer a loss because of someone else's criminal actions, you have the right to seek redress, under civil law, through the courts. So, theoretically, you might have a claim against the dealer.
In practice, any civil action against the dealer is going to be difficult to pursue, partly because you would have to prove (based upon 'the balance of probabilities') that the vehicle was unroadworthy at the date of purchase. (The fact that it was unroadworthy 6 weeks later is not, in itself, proof of this).
It might be worth speaking to someone at your local Trading Standards Office, to see if they'll assist you in seeking some form of compensation, but I wouldn't hold out too much hope. (If you do want to contact Trading Standards, and you don't live within the boundaries of a 'unitary authority', you need to contact the county council, not the district council).
In situations like this, it's often better to apply pressure through an 'unofficial route'. I'm not recommending 'sending the boys round' but it's often amazing how quickly these sort of situations can be resolved if you get the local press involved ;-)
Chris