I think the following is correct:
As part of your consumer rights, any vehicle faults that occur within 6 months are deemed to have been present at time of purchasing the vehicle - Regardless of any warranty.
However, you have to give the dealer fair opportunity to correct any faults - Do not just get it fixed & present him with the bill or you could be left carrying the can.
Put everything in writing, so that if problems are not resolved to your satisfaction, you at least have proof + a time line of events.
There seem to be plenty of decent traders posting on this site who might be able to offer advice from 'the other sides' point of view.
Good luck