Feather #3, it's not quite like that in the UK. Traditionally - that means that's how it was when I was a trainee many years ago - Airport Fire Service attend in the first instance, external services arrive and take over and, if situation does not require their assistance, the AFS return to station, replenish and provide cover for airport operations. ATC remain in charge but will do whatever assists the emergency services - commonly stopping other operations and giving fire vehicles etc a free run if it's serious.
In reality, it's all a bit different but I think that remains the technical answer in this part of the world.