No doubt they could get some form of bulk discount and has already been noted, there are testing stations at many UK airports. However, there is always a cost at some stage - if not direct at source (the customer) then we all pay through general taxation in some form.
So here's a thought - why not add another £50 or so to APD. People who want to fly pay without the rest of the population picking up the tab. Limited means to avoid it and so likely to get better take up of the test.
I think it would be an understatement to say that it would not be popular idea with the airlines or airports who rightly see APD as a deterrent to flying and is already one of the highest in the world.