Rights on being asked for ID in shops?

Hello,

Could anyone tell me if shop staff have the right to ask the person I'm with what relationship they are to and then ask them for ID whilst I'm the one being served?

The store in question is b&m and to be clear I'm 41 and wasn't being challenged for ID but my girlfriend was with and stood behind me while I tried to be served. At no point did she ask me to get anything for her or say anything that would imply I wss buying anything for her, in fact she stood there silent the whole time.

I'm extremely unhappy about this as it created a massive scene with the security guard coming over and other staff surrounding me and lots of other customers all around to witness what was happening.

I the end I told them to keep their goods and walked out of the shop.

Have I got any rights to make a formal complaint against the staff or is it pointles?

Thanks