Military Aid to civil power is a very complex gig which can range from free through to very expensive bills. The reason costs are recovered is two fold - firstly to prevent local councils planning on calling out the military at their beck and call (which also supports local plant hire companies and the like) in order to provide a general pool of manpower.
Secondly cost recovery occurs when stores are expended and people taken off tasks in order to spend money to buy new ones. E.g. we wrote off several hundred sleeping bags a few years ago in some floods for the council to distribute - given they were bought for the military not the civilian population, its not unreasonable to charge the council to buy replacements.
The whole area is a complex shade of grey as there are times when charges wont be made, and other times when partial costs are recouped (e.g. fuel and T&S but not salaries), and other times full costs (e.g. salary and everything spent). The aim is to make authorities plan sensibly for civil contingencies and not rely on the white knight round the corner .
Its also worth noting that there is no charge associated with imminent risk to life, but strangely some of the requests like 'can the military come and build our adventure playground during the week' or 'can the military come and help us dig our cars out of a muddy car park at a civvy show' (both genuine requests) would be met with either a polite 'no chance' or 'yes and to get our services would cost £X).
For those with insomnia, try reading JDP2-02, a worthy read.