The bank of mum and dad is tightening its lending criteria as the credit crunch bites, according to AXA.
The insurer claims that around five million parents (38 per cent) have taken measures to combat tough times, with the result being that children are now feeling the effects of the economic downturn.
Alison Green of AXA said: "Over half of the teenagers we polled said their parents give them money if they run out and one in five knows they will get what they want if they are persistent enough. So there are plenty of young people who have got used to getting what they want, when they want it.
"But all that may change as parents find their finances stretched to breaking point for the first time in years. Parents are getting tough and kids are not going to like it."
Some 2.2 million parents (17 per cent) have made cuts to their offspring's pocket money and some have stopped it altogether.
A further 21 per cent of parents - around 2.8 million people - claim to have encouraged saving.
Teenagers are the most likely to have their cash requests turned down, with one in ten parents of 16-18 year olds saying they have stopped lending money to their children altogether.
Sean Gardner, director of MoneyExpert.com, said: "The Bank of Mum and Dad is perhaps more exposed to an economic downturn than most.
"Parents are being pulled in all directions - rising fuel and food prices, expensive remortgage costs and the overall cost of borrowing are taking their toll. So it makes sense that eventually the downturn would affect children.
"Children who are being encouraged to save shouldn't be downhearted though. Savings rates are sky high at the moment and there are plenty of good deals available for under-18s. The average interest rate on a regular saver account for children is 5.4 per cent."
Younger parents and those approaching retirement are most likely to cut spending on their children, with almost two thirds (63 per cent) of 18-24 year old parents and two thirds (66 per cent) of 55-64 year old parents say they have had to change the way they hand out money to children over the past six months.