There's a lot of odd thinking on this thread. For a start, there's no such thing as places where you can 'only graze sheep'. If you didn't graze sheep the land would not simply disappear but would be a haven of various grasses, heathers, hardy shrubs and forest, attracting all sorts of animals and insects. Livestock are not the only animals that fertilise the soil, reducing the need for chemical fertiliser. I think we can all be a bit human-focused about this stuff sometimes and forget that land needs stewardship rather than complete control at all times.
It bothers me that people say, 'we just want to find a decent way of farming more environmentally' but as soon as you say, well, we could try limiting the demand for meat and returning some of the land to nature, everyone just closes their ears. I'm also in favour of sustainable farming but insisting that livestock are centre stage all the time is not helpful. Finding other more sustainable sources of protein has to be a priority.