I share the concerns over the illegal persecution of raptors and I would encourage anyone with information about it to report what they know to the authorities. I believe that the Government's commitment to tackling wildlife crime was highlighted by its decision to fund the UK's specialist National Wildlife Crime Unit fully until at least 2020.
With regard to concerns about the impact of grouse shooting on moorland, game management can be seen to contribute to biodiversity by providing cover for wildlife, and through the creation and care of habitats such as woodland, grouse moors, beetle banks and hedgerows.
You may be interested to know that the vast majority of grouse moors that are sites of special scientific interest are now in favourable or recovering condition, whereas only around half were in that state in 2006. This reflects growing awareness among moorland managers of the importance and sensitivity of upland biodiversity.
Game management does play a role in the rural economy, generating income and employment in some of our most remote communities. For example, shooting contributes in the region of £2 billion to the rural economy and supports the equivalent of around 70,000 full-time jobs.
Update: November 2016
I am aware of concerns over peat burning, but this technique is considered to help maintain healthy heather at the range of heights needed to provide diverse habitats.
A 2013 Natural England study found no direct evidence relating burning to downstream flooding, and grouse moor owners are carrying out ditch blocking, which can help restore peat, guard against flooding and capture and store carbon.