I think you would be very pleasantly surprised at how many people will do just that. The 744's at LHR have not yet had anything done to them that would require additional work to get them back to passenger standards either, they are simply stored and very importantly, they were stored using procedures fully expecting them to fly passengers again. The main difference between flying them empty to CWL or with pax on board is a full and currently rated CC are needed.
Just needs a will to make it happen......exactly as QF have done who are facing the exact same issues as BA regarding Covid19 restrictions, having to make staff redundant and a possibility Greta jumping up and down. No difference whatsoever, the PR angle by BA simply needs to be a) the flights are going to happen anyway because they must be flown out of LHR and b) they are charging money for the flights and for each flight, the income received is greater then any costs.
Can you enlighten us what the "high costs" are as they have been stored using procedures that fully expected them to return to pax service?
The costs have been highlighted above. This won’t earn BA any money at all and I personally doubt there is sufficient demand at a time like this for a twenty minute flight.