Sometimes in England a landlord will be attempting to illegally evict a lawful (non-squatting) tenant, so the tenant calls the police for help and is surprised when the police assist in the illegal eviction! Obviously this is not supposed to happen. The police should not be evicting people just because some random told them he owned a property and it was being squatted.
On the other hand, the legal situation for evicting squatters in your home isn't so bad here. You have 28 days after you find out you are being squatted, and the eviction only takes 24 hours.
Unless you register all tenancies with the state (which seems like massive overreach) how can the police quickly determine the lawful possessor?
You already effectively have to do that, landlords are supposed to pay taxes on the rent, and people are required to register where they live.
Then squatters move in in two steps. First they do a small break in and leave, observing whether someone notices and fixes the first break in. If the first break in goes unnoticed, it is probably safe to move in, change the locks and squat there permanently as nobody will confront them in the 48h window.