My guess is that the wild animal that poses the worst threat to a cat in the UK is probably a badger. Maybe a Scottish wildcat, though those are very rare and remote, and it sounds like those are more likely to mate with a housecat.

It does sound like the American badger, while smaller than its European counterpart, does tend to go more in for hunting, though:

https://a-z-animals.com/blog/american-badger-vs-european-badger/

Might be something of a wash there.

EDIT:

They also do have the adder, but we've got rattlesnakes, copperheads and cottonmouths, and I'm pretty sure that those, particularly some rattlesnakes, would be more dangerous.

https://en.wikipedia.org/wiki/Eastern_diamondback_rattlesnake

The eastern diamondback rattlesnake is the largest rattlesnake species and is one of the heaviest known species of venomous snake, with one specimen shot in 1946 measuring 2.4 m (7.8 ft) in length and weighing 15.4 kg (34 lb).

The eastern diamondback rattlesnake has the reputation of being the most dangerous venomous snake in North America.[40] While not usually aggressive, it is large and powerful. Wright and Wright mentioned a mortality rate of 30%, but other studies show a mortality rate of 10–20% (untreated).[18][41] The eastern diamondback rattlesnake is a major leader of fatal snakebites within its geographical range.[42]

And that's mortality for humans, which are a lot bigger than a cat.

https://www.pdsa.org.uk/pet-help-and-advice/pet-health-hub/conditions/snake-bites-in-cats

Fortunately, adders tend to keep themselves to themselves and don’t bite unless they are scared.

If your cat has bitten by an adder, their symptoms will depend on where the bite is, and where the venom spreads to. If the venom stays in the tissues around the bite, it will cause pain and swelling, but if it spreads further and gets into the bloodstream, it can cause much more serious problems such as damage to the liver, kidneys, heart and nervous system. If venom is injected straight into the blood stream, it can cause death very quickly. It can also be very serious if your cat is bitten on the face, tongue or neck because swelling can lead to breathing problems.

With treatment, most cats make a full recovery, but sadly, in some cases, adder venom can cause severe illness and even death. The quicker your cat is treated, the better their outlook. Any cat with a suspected adder bite should be seen by a vet ASAP.

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.