The fall out from the London fire shows how unprepared many Borough Councils and County Councils actually are. Once upon a time I was a Borough Councillor on a home counties Council and I know they had plans in place for such an event even to the extent that that held emergency exercises at least once between each election.
During my time the exercise was a passenger plane crashing on a sports centre (it had to be council property for ease!) which was not as daft as it sounds as the location was near to the normal take off flight path of a well known Bedfordshire aerodrome (ask your dad) used by a few holiday makers and freight organisations. The Council has it’s own emergency room in the basement of the civic centre complete with secure land line links and a (currently disused) radio transmitter for backup communications. Obviously the building dated back to the sixties and from what I saw would not take a lot to get back into use. The Chief Executive was the designated coordinator who was expected to bring in staff and involve councillors for the ward(s) that any emergency occurred. First response was the idea so that the events that happened on the 14th should not have happened and help should have been on the ground by mid morning at the latest.
As you all know, I live in a perfect world where nothing goes wrong (hence the plaster cast on my wrist this month), but maybe you ought to ask your local councillor if they have any procedures in place in the event of a similar emergency in your Borough/City.