.Bullfrog…have nothing but sympathy for your point of view which sadly all too prevalent in the UK and is in my view more of an excuse, rather than any real attempt at protecting data. .
I recently had an issue with a duplicate booking in club to Europe. After making a redemption booking I changed my mind and bought 4 club seats for myself and the family. Then tried to cancel redemption booking but could not as BA.com was having one of its many off days as you have experienced today.
Called BA and got a charming lady and explained the issue. My redemption booking was separate from the family but she cancelled without a problem and at no charge due to being Gold Card she explained. All was well
When it came to my wife and kids it was a very different matter and this charming lady quickly became an automaton when the data protection act reared its ugly head.
That I could provide PNR details, logins for each executive club account, dates of birth, e ticket numbers and inside leg measurements, counted for nothing. More bizarrely still was that all four of us were booked on the same flight under a single PNR. This was still not good enough and they refused to even discuss it, but were happy to talk to me about the duplicate booking and accept it was indeed a duplicate of 3 in club on the same flight.
My revenge has been to leave the redemption booking in place and cancel at -24hrs via phone they have 3 seats in club blocked for sale and through their own inflexible attitude will lose revenue if they are not sold.
Like you I have respect for the laws but common sense must prevail and I have neither the time not patience to deal with this sort of nonsense.