LibDem MP Annette Brooke is hoping her private members bill will succeed where similar bills from MPs Peter Bone (Tory) and Eric Martlew (Labour) have failed.
The MP for Mid Dorset and North Poole presented her bill to Parliament yesterday. She said it "aims to protect children from head injuries, and the devastating effects of brain injury, by making it compulsory for those under 14 to wear cycle helmets."
Children climbing trees, or travelling in cars, or walking on streets, or skateboarding, or riding kick-scooters, will not be required to wear helmets, her proposed measure is just for cyclists.
The Cycles (Protective Headgear for Children) Bill will make it mandatory for children under 14 to wear cycle helmets when cycling on roads and in open spaces.
She said: "The law will not criminalise those cycling without helmets, instead requiring proof of purchase of a helmet within 28 days to avoid a fine.
"We have a duty to protect our children, and the Cycles (Protective Headgear for Children) Bill will do just that. Brain injury devastates the lives of individuals and their families. Children are at a higher risk because not only are their brains not fully developed but they are less experienced at cycling and on the roads in general."
The MP does not propose any measures to prevent the risk of cycling on roads, such as slowing down motorists.
"Brain injury lasts a lifetime. We owe it to children to protect them in the years before they are old enough to make their own minds up," said Ms Brookes.
"More children wearing helmets will mean a reduction in child deaths and serious brain injury. Through this Bill I hope we can make cycling even safer, and encourage children to get out on their bikes."
Studies have shown that forcing children to wear helmets has the opposite effect: reducing the demand for cycling.
The MP's bill has the support of the BMA, brain injury charity Headway, the Bicycle Helmet Initiative Trust, Child Brain Injury Trust, road safety charity BRAKE, and the Child Accident Prevention Trust.
No cycling groups are in favour of cycle helmet compulsion. And Brookes does not have the support of key LibDem MPs.
Julian Huppert, LibDem MP for Cambridge, and co-chair of the All Party Parliamentarty Cycling Group, said:
"The Lib Dem transport team disagrees with her. I've tried to persuade her! Lib Dem (& coalition) policy is not to have compulsory helmets."