While training the self-declaration of medical fitness that you signed on the membership form has been sufficient to allow you to fly, but prior to flying solo you need to have a doctor sign a form to confirm that you are fit to fly.
This is not a 'full flying' medical (such as a JAR class 1 or 2), but an NPPL (national private pilot license) medical declaration. No examination is required, and if they start trying to examine you then they do not understand what it is you want. The NPPL medical required for gliding in this country is a check of your records to ensure that there is nothing that would prevent you from holding a DVLA driving license (i.e. the criteria for flying and driving are the same).
Providing you have no conditions that require regular review the declaration will last until you are 45.
The campus medical centre can perform the check, but will charge about £80, as it is classed as non-NHS paperwork.
The form can be found at the following link, and contains guidelines for both the pilot and the GP:
http://www.caa.co.uk/docs/33/SRG1204.pdf