While the flights may be operating under BA flight numbers in appearance its not the actual case. If the aircraft is still painted in the BD livery and still on the BD AOC then the BD call sign and flight number is still used, to the passengers it's a BA flight but it's still BMI crew in BMI uniforms.
For factual accuracy. The aeroplane can be painted in BD colours, but still be operated on the BA AOC. The aircraft's registration on either respective AOC is the only determining factor I believe!
And of course,
ALL crew are BA crew now, regardless of whether they are temporarily wearing another airline's uniform.