As said above you should go back to the dealer. You have legal rights but you must not try to fix it yourself before giving the dealer the opportunity, as that would allow them to argue that you caused the problem.
Be prepared for them to say that you should have noticed any fault before buying, but I think you can argue that it’s unreasonable to expect you to check everything.
The Consumer Rights Act gives 30 days in which you can return the car for a refund if you’re unhappy. A local Citizens Advice Bureau can give more detailed advice.