The heathland (heather mainly) in the New Forest is managed by the Forestry Commission using "controlled burns" - this prevents the heath from being turned to scrub and promotes new growth for the ponies and cattle to feed on. However, it is done in the spring when the ground is still wet. If the heath was burned in the summer when the ground was dry the soil itself is scorched and the regrowth takes much much longer to happen. So its not really in the interests of sheep farmers to start fires on the moor during dry weather, unless they see it as any burning is better than no burning at all. More likely to be ignorant idiots (cigarettes, ill advised barbecues or campfires) or malicious idiots (twisted firestarters).

As for bracken, in ye olden days commoners would harvest it for various now obsolete. In places the FC has started spraying areas of heath with some kind of herbicide that kills bracken but not other heathland plants, like gorse and heather.

There was some palaver about a heath fire scorching the stones at Tregeseal East near St Just in Cornwall a few years ago, mainly focusing on the damage to the rare lichen on the stones (rather than the stones themselves).