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About £7.1m a year is spent on tackling childhood obesity but the bill could rise to £111m if they become obese adults, a London Assembly study found.

One in five children in London are obese, which is higher than the England average of 18.7%, the report said.

But obesity was linked to deprivation with well-off Richmond having the lowest rate at 12% while 28.6% of 10 to 11-year-olds in Westminster are obese.

The study urged Mayor Boris Johnson to take a coordinated city-wide approach.

The mayor's office said he was working towards a "pan-London initiative".

The study, commissioned by the Health and Public Services Committee, found 240,000 children in London were obese.

It found 11.6% of four to five-year-olds were obese which increases to 21.8% in the 10-11 age group. Another 160,000 children are overweight.

The rate of obesity has jumped in the past 15 years and boys were at greater risk.

Children in the Bangladeshi, Black Caribbean and Black African communities were considered high risk, but obesity was linked more to deprivation than ethnicity, the report found.

Westminster (28.6%), Southwark (26%) and Newham (25.9%) had the highest rates of obesity in the 10-11 age group.

While in Richmond, only 12.1% children (aged 10-11) were obese, followed by Kingston at 16.7% and Bromley at 17.2%.

The report said if 79% of these children became obese adults, London would spend £110.8m tackling the problem annually.

Committee chairman James Cleverly, said: "London has the highest percentage of obese children in the England and obesity prevalence has increased sharply in recent years.

"There is a strong case for the mayor to intervene on this issue and we want to see a new obesity strategy for the capital."

The report found the mayor has undertaken several initiatives, but lifestyle counselling by GPs, walking schemes and school bus programmes were the least effective while those combining dietary advice and physical activity worked best.

The committee urged Mr Johnson to formulate a new coordinated strategy by 2013, set out funding beyond 2012 and to evaluate current initiatives through the new London Health Improvement Board.

Pamela Chesters, mayor's health advisor, said the mayor was "delighted" by the prospect of the new board under his leadership.

"It will be possible to make real inroads into the health challenges affecting the capital, including childhood obesity," she added.

The new board will meet this summer to determine its priorities.