Devil's Bridge in Kirkby Lonsdale is a popular spot over the River Lune for "tombstoning", which involves leaping from height into water.
A by-law prohibits jumping off the bridge but town councillor Paul Stephenson said it was being ignored.
Sgt John Stephens from Cumbria Police said landing in the river from such a height was like "hitting concrete".
He said: "People think it's similar to jumping off the side of your local swimming bath into the water.  Well, it isn't.
"It's bad enough hitting the water at speed from such a height but, if you hit a rock, obviously that's got dire consequences."
He said the police could only issue fines if they catch people in the act and appealed for anyone seeing it happen to report it.
Mr Stephenson said: "When the police come down, they all stop.
"The police can enforce the bye-law to stop them jumping off but the police obviously aren't there all the time."
Thrill-seekers are still jumping off a 40ft (12m) bridge in Cumbria where a man died last year, police have said.