How to persuade these people to do what we'd like regarding their land?

Seeing as the land is S.S.S.I. it is very unlikely that planning permission will ever be granted. However there are forestry schemes running at the moment encouraging landowners to plant up areas of land with native trees and plants and once established giving the public access to the land so the fact that it is being left to return to the wild doesn't bode in your favour. Contact your local council to check out their planning policy and also mention the fact that you are having problems with vermin. Putting out rat poison yourself isn't ideal as chances are that other animals other than rats will pick up the bait. If there isn't any chance of houses being built then approach the land owner and ask, the worst they will say is no, meaning you are no worse off than you already are. But if they do want to sell, no doubt they will charge a ridicuous amount of money, just because they know you want it.