It's a completely different financial setup here Bert; medical care free at the point of delivery, very little privately/insurance funded work in the provision of trauma care. Also, the geographical nature of the UK can mean that some areas are really quite well covered by A & E [ER in the US] services. That's where the main thrust of the aforementioned academic work lies, in that yes air ambulances in the UK can make a difference but sometimes that difference is quite small and therefore hard to justify funding from the state.
Our area for instance has 7 A & E departments for a relatively modest area and population. The local air ambulance is on ten hours a day and responds about a thousand times a year; I don't know the rate of cancellations/non-serious tasks but to be honest that shouldn't bother the ambulance authority because the service is paid for by local people. The local police unit, empowered to respond to serious cases for the other 14 hours a day, for free, has been used by the ambulance authority 12 times in the last 4 years. Despite efforts at the local level, inter-emergency services management co-ordination remains very poor, at least in our area.