Hen harriers do like to nest on grouse moors in this country, but doing so gets them shot. Read about what happened to Bowland Betty, one of the handful of hen harrier chicks to fledge in Britain in 2011. (It is a pity that our hen harriers seem so set on breeding in moorland. My sister lives in southern France and there are hen harriers nesting in an arable field a stone's throw from her home.)
I'm all for looking after the full biodiversity of every habitat that we have in the UK, whether natural or not so much, very species-rich or not so much. Upland grassy moor is also valuable habitat (if not overgrazed). Unfortunately, as other posters have said, commercial grouse moors are managed to look after only red grouse, at artificially inflated numbers, and any other species that might impact on grouse numbers are not tolerated. Here's a quote from the head of species and land management at RSPB Scotland (and remember that the RSPB are not anti-shooting).
"We have seen major intensification of management practices on many grouse moors in the central and eastern Highlands and Southern Uplands of Scotland.
"This moorland management places emphasis on increasing the numbers of gamekeepers, to undertake high levels of predator control, more frequent and extensive heather burning, veterinary medication of red grouse, and the killing of mountain hares and deer, ostensibly to prevent tick-borne grouse diseases.
"It would be far more appropriate to describe this activity as 'grouse farming', with monocultures of heather habitat producing unnaturally high grouse shooting bags.
"Indeed, we do not believe that is possible, whilst continuing to operate within the bounds of the law."