The police don’t do that in the first place, it’s a paranoid myth that ignores the serious infringement on privacy in the UK.
Meanwhile those on an anonymity crusade have to show their phone provider legit ID (driving license, passport) to open up a porn blocker and provide every ID provider in the country evidence of where they’ve lived in 3 years in order to get anywhere. Meanwhile the police push for unfettered access to government databases.
The police aren’t stopping and searching because they need an ID card to ask for. They have plenty to go off already.