Feather... not quite correct, at least as far as the UK goes. If airfields had to shut every time the AFS turned out not much air traffic would move. At Heathrow - and probably everywhere else in the UK - there are set positions on the airfield where the safety services will standby. In getting to those positions ATC will provide separation between the safety vehicles and other ground traffic. However, everything certainly does not stop. The AFS may wish to enter the runway to follow and aircraft and this is agreed with ATC. There is liaison between ATC and the AFS by telephone and radio so everyone knows what's going on. At Heathrow where one runway is used for departures and one for landers the traffic on the "other" runway continues normally and this means that taxying a/c continue normally too.