Your GP does not have to give you a medical certificate to show that you are well. There is no 'fit to return' note. As soon as your current 'fit note' runs out without being renewed, this tells your employer that you are fit to return to work.
If your employer wants extra medical confirmation, you should ask your GP to help, but remember that unless your contract says something different, you are entitled to be paid your normal wages as soon as your GP has confirmed that you are fit to return to work, as long as you are ready and willing to return. Guidance from the Department for Work and Pensions states clearly that any extra medical tests your employer wants you to take once you are fit for work must be organised and paid for by your employer.