No.
The police have 101, the health service has (or will have, depending upon where you live) 111 but there's no national number for non-urgent calls to the fire service or coastguard (although, of course, you can find a number for the county fire service HQ or for HM Coastguard offices).
Anyway, the fire service regards all fires as 'emergencies' so you've no need to feel guilty.
Although, as the end of my post here shows, it can still be rather embarrassing when you call the fire brigade . . .
http://www.theanswerbank.co.uk/News/Question515427.html#answer-2468923
;-)