Rats like my apple trees. Advice?

I have 5 young apple trees in my garden and the last 2 years have seen good production.

First good year I saw a rat in the garden, trapped it. No sign again.

Second good year:
I noticed that fallen apples disappeared slowly but then noticed nibbles out of an apple on a tree 6ft up.

I thought it was birds - they love pecking at the cherries from a tree in the front.

I then saw a small rat in the garden, which alarmed me. I thought it was after the fallen apples but I'd started to pick them all up. [I set a trap again but no takers]. Days later I saw a rat run up one of the trees to get at the apples! I picked all apples from the trees and then no sign of a rat at all nor in the rest of the year since.

So obviously I have a rat/apple problem. Has anyone else had the same problem - and how do you solve it? I feel like cutting the trees down but that's a bit drastic! Any ideas please? Thanks.