If the council are anything like the one we've got here and they want to look at litter, then maybe they should follow their own dustcarts on dustbin day.
I guess it all depends on what you consider to be litter - a can, plastic bags etc are one thing, but bread, apples, kitchen scraps could also be considered litter. Given that the couple are wildlife trust and RSPB members, I'd be surprised if the litter was the former.
If there had been signs about not feeding the birds, the council wouldn't have to issue a fine for littering, they would have fined them in conjunction with the notice.
The Telegraph story mentions the 42-year-old wife, but regardless of who it is, the complaints were about large numbers of birds, no mention of rats etc.
Unfortunately, this sort of thing would appear to be quite common and whilst working as a rural surveyor I've often come across city dwellers with second homes in the country who don't like cows, the morning chorus, duck ponds, people feeding the birds, people walking in the fields at the back of their house etc. There's probably a lot more to the story, but 4 days monitoring seems a bit of waste of time if nothing else.