The Consumer Rights Act is your protection.
Find out about it here:
Learn about our National Consumer Campaign, where we work with partners to raise awareness of different consumer issues.
www.citizensadvice.org.uk
There are helpline numbers provided so I suggest that after reading about the protection you have in this situation you give them a call.
The fundamental principle is to start a diary/log of all your discussions with the company recording what was said by whom and when. Take photos of the problem.
Write a letter, not an email, and hand deliver it or send it signed for outlining the problems and stating how you wish them to be resolved. Give them a deadline to fix the issues, say 14 days.
The warning lights will result in an MOT failure so they must fix the problem.
Bottom line, don't take No as their answer!