In descending order of likelihood (most common towards top of table) here are the birds you might reasonably expect to see.
Of course it all depends on where you live in the UK. The birds in Wales are quite different from the birds in North East Yorkshire. You won't find recently re-introduced Sea Eagles in Milton Keynes but you will on the coast of Scotland!
Other wildlife in your garden
Hegehog [common] - have a resident hedgehog in my garden.
Fox [fairly common] - seen at the Open University (Milton Keynes) many times.
Badger [uncommon] - never appeared in my garden or anywhere near me!
Squirrel (Grey) [common] - yup, got one of those.
Squirrel (Red) [rare] - I wish. There are still pockets of them but if imported, American grey squirrels are present too, then the native British red ones will be forced out, eventually.
This list wil be updated as time goes on. If you have an unusual visitor do let me know and I'll add it into the list. Tell me where you live (in the UK, I don't need to be told about American Eagles in Texas, thanks all the same) so others can tell if it is worth looking out for them.