A 91-year-old woman who called officers after her home was besieged by yobs had to wait 36 hours for police to turn up.
And a couple who were ambushed by a gang of teenagers brandishing sticks and baseball bats were told the police were "too busy" to come out.
The horror stories came as it emerged £10m raised by speed cameras in Yorkshire each year is being handed straight to the Treasury – instead of being spent on policing in the county.
The cash – made up of thousands of £60 fines – would be enough to pay for an extra 470 officers on the streets.
But none of it is being spent directly on tackling crime and instead it is being ploughed into installing more camera traps.
Today's revelations follow a YEP investigation which showed that West Yorkshire is being policed by just a few hundred more officers than it was 25 years ago – despite a three-fold increase in crime. We also found that the region now has the lowest number of police per head of population of any comparable force in the country.
On Saturday night the reality of those shocking statistics hit home for pensioner Elsie Ward who was left cowering in her first floor flat as a gang of yobs ran amok outside.
The terrified pensioner waited in vain for the police to turn up – but no-one arrived.
"I've never been so frightened in my life," said Elsie of Beeston, Leeds. "They were at the window shouting and swearing and banging till late into the evening.
"I was too scared to go out but I didn't want to stay in either. I'm 91 years old – I shouldn't be left to suffer like this." The police arrived 36 hours later.
And today Chief Supt Sue Day, of City and Holbeck division, apologised to the pensioner, saying officers could not attend immediately because of a "high volume" of jobs: "I am very concerned at the quality of service that Mrs Ward received and I will be looking into what went wrong," she told the YEP.
In a separate incident, Garry Coldwell and his wife, Rachel, were ambushed by a gang of teenagers brandishing sticks and baseball bats as they drove a friend home along a quiet road.
The yobs were standing behind a barricade blocking New Lane, near Tong Village, on Sunday evening. A friend phoned the police on his mobile – to be told they were too busy.
A police spokesman today told the YEP that the force was aware of the incident and had turned up about 40 minutes later.
But Rachel, 32, said: "The person who answered the phone gave us a crime number and that was it. He didn't seem particularly interested and said the police were busy at a fire in Leeds. They never even got back to us to make sure we were all right."
The incidents come after Chief Constable Colin Cramphorn admitted there were "serious questions" about police numbers in West Yorkshire and warned the public that they had to be prepared to pay if they wanted a "first class" service.
But arguments over funding are of little help to Elsie.
"I felt totally on my own and really vulnerable." said the 91-year-old. "I know the police are busy, but I just wanted the youths moved on so I could get a bit of peace and quiet.
"You'd think at my age I'd be allowed that."
matthew.taylor@ypn.co.uk