Given the total confusion it is a brave man to give definitive advice in the UK....
My understanding is that medical care is a valid reason to break staying at home. The rules up until yesterday specifically allowed people to enter the UK and avoid quarantine if they were going for medical treatment. That is all it said because it assumed the individual would remain in hospital and the hospital would be lumbered with any decisions. Of course many people came into the UK for an out patient consultation, whilst almost all the others left hospital well before the end of 14 days, and we advised them to quarantine except for attending medical care, but nobody would give us definitive advice, possibly because nobody had thought it through.
The issue here is whether renewing a certificate where there is no illness and the occupation it allows is not essential is covered by the term 'medical treatment'
However as the police dont understand the rules and the rules are so poorly drafted, the individual will have to use his own best judgement as to whether his visit is allowed or not.