I was at an ABS club meet at South Mimms many years ago when a car (not one of ours) started smoking in the car park. After a few minutes it was clear there was an under-bonnet fire. We used our own personal in car fire extinguishers to try and put it out - but after perhaps 5-7 of them it was clear we were having little effect. In the end we had to all back off and wait for Hew, Pew, Barney McGrew et-al to turn up. By the time they did the car was well alight inside and out. It took them a few minutes to put out the fire once they arrived, and AFAIK no other cars were harmed.
I know the airfield fire service at RNAS Yeovilton do respond to (very) local incidents around the Yeovilton/Ilchester area, but civil Fire Brigade also have to attend. I don't know what happened at Luton, but if you drag the airfield fire service off station then the airfield may have to stop plane arrivals and departures coz there is insufficient fire cover. Places like Heathrow have (IIRC) three separate fire stations so they can continue flying even if one station is dealing with a shout. Luton, being only one runway, may not have sufficient cover to handle two events at the same time.