A cougar in the Americas eats anything it can overpower: mice, rats, rabbits, raccoons, possums, deer, any number of bird species including domestic fowl, also they will take young cattle, sheep, goats, and on very rare occasions have been known to kill humans. The latter probably sick or starving animals as they generally avoid human contact.
Many big cats are opportunists, England has lots of exotic waterfowl like Canadian and Egyptian Geese and native ducks, rabbits, deer and so forth. It is also heavily wooded and sparsely populated in certain areas.
My objection to big cats being in England is the same one I use against Bigfoot in the States: by now a big cat would have likely been killed by a car; they are killed by cars in the U.S. even though some, like the Florida Panther are very rare. The automobile has proven to be their top "predator," sad to say.
Big cats are the UK equivalent of Bigfoot in the US. People have been claiming them for years, but not a shred of scientific evidence to support the claims. As with Bigfoot, The longer we go without evidence, the less likely it is that they exist.