The UK is Europe. Always has been, always will. Shifts in tectonic plates would have to happen to change this.
Cats have been in the UK for far longer than the Americas were colonised. The UK doesn’t have much of a natural ecosystem to protect in the same way the Americas still have. Despite that small cats have always been part of the ecosystem in the UK. We have wild cats, they are one of the last predators that aren’t pests we have in the wild. Our lack of predators is a problem, to the point people want to reintroduce wolfs.
So your wrong on both accounts. Letting cats outdoors is fine in the UK. Some animal shelters won’t let people adopt cats if they live in a flat and can’t let the cat outside.
Cats even have right to roam protections that are greater than most people in the UK have. Cats can’t trespass, so you can’t take action against them on your property.
The biggest threat to the local ecosystem they pose is breeding with wild cats. But is always recommend to neuter outdoor pets. Most birds here have always had the threat of small predators, and most of the birds are domestic breeds of pigeons that are pests.