At most UK airports (certainly the larger ones) wildlife control is not carried out by the fire service.
A range of ways & means are used dependent on the particular problem at that airfield.
Most "resident" birds are not stupid and using only one method of control doesn't work very well at all.
Personally I'm not convinced that having a dog wandering around loose near runways is a bright idea.
A person walking off a lead is likely to be just as effective and slightly less unpredictable
As for birds of prey .. hawks can be effective in a limited way ... problem is once they've had a fly around and eaten that's it for the day(s).
They can be useful as a way of varying the deterrent which is what you need to keep the beggars guessing.
Bird control is all about manging the environment first and then making it easier for them to go and eat/sleep/breed elsewhere rather than on your airfield.