Appeal against failing the drink drive medical test
Your test results for the drink drive medical test will be sent to DVLA. However there are no internal appeals procedure at the DVLA should they decide to refuse returning your licence to you. You can however appeal at a magistrates court at your own costs and will need resonable grounds for appealing against the decision of the DVLA. You can have a Liver Function Test done privately and if the outcome is positive use that as evidence that you are clear (or have been cleared) of alcohol for a while. You may wish to discuss this with a solicitor specialising in drink driving before you go to the courts though.
You can find more information on licence restoration at the DVLA website.