You can appeal against an MOT failure if you believe that your vehicle should have passed. If you decide to do this, your first step should be to speak with the test centre manager; they may be able to resolve your issue.
If you are still unhappy with the outcome, you should complete a VT17 form (downloadable from the gov.uk website) with details of why you wish to complain about the MOT test. You should email the form to csccomplaints@dvsa.gov.uk. Alternatively, you can send the form by post to:
DVSA, The Ellipse, Padley Road, Swansea, SA1 8AN.
The DVSA should then contact you within 5 working days to discuss your appeal. If they determine that a retest is needed, you can then arrange a new MOT test. You will be required to pay the full test fee again. However, if your appeal is ultimately successful, you will be refunded some (or all) of the fee.