I was going to agree that you won’t meet any dangerous wildlife in the UK, but that’s only 99% true. Assuming you aren’t stupid enough to try and pet a badger, we don’t have any rabies, but we do have a couple of areas with established escapee wild boar (I don’t recall hearing of any attacks though). We also have deer and rutting stags can be dangerous.
The main animal risk for dog walkers is actually farm livestock, of which we have a lot, and I remember an American posting in horror on here about having to walk the dog on footpaths (as in public access routes through private property) through farmland. Dogs must always be on leads near sheep for the sheep’s safety, and you should be aware of how to take them through fields with cattle and horses safely - or turn around. More people are killed/injured/scared by these than any wildlife.