Firefighters in Manchester said on Sunday that strong winds were consuming all their resources.
The service said it was being "seriously tested" and received 126 calls in three hours as winds battered the northwest of England.
The service stopped short of saying it couldn't respond to any more incidents, but told the public to call 999 only in an "actual emergency".
Dan Simms, a spokesperson for Greater Manchester Fire and Rescue (GMFR), told BuzzFeed News the service was "severely, severely stretched". Asked whether someone who called 999 on Sunday afternoon would have been turned away, he said: "We're an emergency service, we have to prioritise calls we receive, and obviously if someone's life's at risk that will be the priority.
"If it's a bit of scaffolding lying over a road in Stretford we're less likely to prioritise that over someone being stuck in a fire, or someone who needs rescuing from a car crash."
Simms said the tweet was to help people understand that "we are stretched" and that the service had a limited amount of resources, "which are shrinking because we are being cut a lot".
He wouldn't confirm if or how many callers were turned away or told to wait.
GMFR said a 50ft tree in Salford fell on to some flats, while the roof blew off a row of shops in Denton.
The extreme weather's drain on the service's resources was used as evidence to say firefighters shouldn't face more cuts.
GMFRS planned to save £7 million in 2014–5 and was scheduled to reduce its budget by a further £13 million by 2016 as a result of reduced government funding.
Patrick Smith is a senior reporter for BuzzFeed News and is based in London.
Contact Patrick Smith at firstname.lastname@example.org.
Got a confidential tip? Submit it here.