According to this lot...
Peak District National Park Authority, National Trust, Natural England, United Utilities, Severn Trent Water, Environment Agency, Derbyshire County Council, Sheffield City Council and Moorland Owners:

The main causes of accidental fires are arson, discarded cigarettes, campfires and camping stoves, out of control managed burns, and in some rare cases, lightening and sunlight magnifying on broken glass. Statistically it appears most fires occur at weekends, especially Saturdays, and near to footpaths.
Hmm.... near to footpaths - where human traffic is steered - rather than on the free-to-roam access land.

Meanwhile, over on the The Peak District National Park Authority's site...

Walkers can act as a useful fire watch and give early notice of the danger particularly if carrying a mobile phone. Accurate information on the location with map reference or bearing can save precious time
So, it may actually be useful at times like this to encourage runners (so long as they're carrying mobiles & can read a map) onto the access land?