These are wet leased aircraft,so if approved they will come with pilots and cabin crew,with perhaps a BA supernumary cabin crew to supervise the service.
From previous experience there will be an issue with the right to work in the UK,both for Pilots and Cabin crew.The CAA does not police visa issues,but they will be looking at the whole operation.Just because Qatar is allowed to operate DOH-LHR-DOH does not mean they can bring a sub fleet here to wet lease.The strike of a percentage of the Cabin Crew insufficient in numbers to shut down the whole airline may not be considered exceptional.
The Home Office or the DoT will be the ones issuing visas.l