My white DH got stopped years ago whilst doing his postal worker job. He thinks it was to do with targets, because he was in full uniform and had his postbag with him. Police officer stopped him, gave him the spiel, some BS excuse for the search, asked him what he was doing and where he was going. DH said, I'm doing my round, told him what it was, and he can be verified by ringing his manager which was declined by the officer. He had his pockets searched, and had a superficial body search.
PO asked him what was in the bag. Post, replied my DH. I need to look in the bag, asked the PO. You can't, replied DH. It's the property of The Crown until I deliver it. (This is true) PO got arsey, demanding to see inside.DH stood his ground, saying if he wants to escalate the situation he can ask his manager to contact the borough commander to ask why his officer is tampering with Crown property. Also, my DH signed the Official Secrets Act when he joined the post decades ago so there was that complication on top. PO grumbled but backed off. DH noted his number, got his receipt and carried on with his job.
I know in the past posties have done dodgy things whilst doing their job but he couldn't believe the PO didn't know the law. Also, he thought it smacked of fulfilling a target rather than having any genuine suspicion of wrongdoing. DH rang his manager about the SnS and the manager complained to the Met but nothing came of it.
Specifically regarding the TSG, who stopped the couple, they are known ar**holes. They are supposed to concentrate on things like protests and large events, which they mostly do, but they have a reputation for overstepping and for using their power inappropriately. Earlier this year the TSG arrested some volunteers who were advocating personal safety by handing out flyers in the West End. The volunteers had permission from Westminster Council to be there but the TSG arrested them anyway.