I don't know what a Dr would say but for info here is the section form the BA CoC:

https://www.britishairways.com/en-gb...ns-of-carriage

3b3) If, after beginning your journey:

• you become ill
• your illness prevents you from travelling on your next flight within the validity period of your ticket; and
• you want us to extend the validity period so that you can continue your journey;

you must give us a medical certificate. The certificate must:

• state the facts relating to your illness and
• confirm the date you will be fit to travel again ('the recovery date').

When we receive the certificate, we may decide to extend the validity period until either:

• the recovery date, as long as there is a seat available on the relevant flight in the class of service for which you have paid the fare or
• if not, the first date after the recovery date when a seat will be available.