Whilst legally PC 4825 wasn’t compelled to give his name, he was rude, arrogant, and bloody awkward which isn’t actually allowed! He held you far longer than necessary because you dared question his authority, and he behaved like a petulant little kid.
I’ve previously worked for the police and know that the vast majority are fine. However, there’s a thuggish minority that need reining in – and 4825 looked like a classic example. BTP carry out more stop and search than nearly all other forces combined so PC 4825 has more opportunity than most to inflict a very unpleasant experience on random members of the public. I strongly suspect that his behaviour that morning was typical, but any other complaint would boil down to someone’s word against his. You have his totally unprofessional behaviour on film.
Please make a formal complaint, which you could later agree to have ‘informally resolved’. Any Commander worth his or her salt would have strong words with our friend about his conduct towards the general public after seeing that film, and make sure he was a little more sweet in future.