NPPL Pilot Medicals

Quite simply, if you are fit enought to drive a car, you're fit enough to fly.
If there is nothing in your medical history which would stop you reaching the Driving and Vehicle Licensing Agency (DVLA) Group 2 standard for professional driving, you can obtain an unrestricted National PPL. Your GP will know these driving medical standards and the most up to date version can be found on the DVLA website. 
If you do not meet the DVLA Group 2 standard for professional driving, but do meet with Group 1 standard for private driving, you will be able to fly either solo or with a "safety pilot".
Your GP is not required to do a physical examination, though he/she may wish to check routine health functions. Their signature is to confirm the lack of any medical history which would stop you meeting the appropriate DVLA standard. Your GP may charge you.
Once the medical declaration has been countersigned by your GP, this becomes your student pilot licence and allows you to fly solo whilst training. When you have got your full license you can then carry passengers if you meet the Group 2 professional driving standards.
Full information and forms are available from this CAA web page or from the BMAA here.