The NHS offers screening, free of charge, to identify pre-existing health problems of which you may not be aware, nor be exhibiting any symptoms. The NHS screening may be as part of a national programme for specific demographic groups or may be opportunistic screening when a patient discusses a related problem with their GP.
Regarding certificates or evidence about your COVID vaccination status GPs cannot issue a certificate to demonstrate your vaccination status. Please see https://www.gov.uk/guidance/demonstrating-your-covid-19-vaccination-status-when-travelling-abroad for further information. Proof of your vaccination status will be available in the NHS app from 17th May 2021, and in some of the other apps that provide you with Patient online services.