You might find something helpful in the following link:
https://www.hedgehogstreet.org/forums/topic/hedgehogs-and-rats/
Be aware that hogs can be quite good at climbing also that traps which catch the rats alive have been known to catch hedgehogs as well.
From what you’ve said, it sounds as if the bird feeding area is the problem. So make sure that is kept clean and tidy and try to prevent any from reaching the ground. If the rat doesn’t find any food, there will be no point in it visiting. Also generally make life more difficult for it by filling in bolt holes, etc.
2 more links but might be repeating some of what’s said in the above:
https://www.hedgehogstreet.org/forums/topic/rat-poison/
https://www.hedgehogstreet.org/forums/topic/rats-3/
