According to a new survey published today, one in three mothers admit that they buy brands or products demanded by their children.
But health organisations warn that children are being heavily influenced by advertising and peer pressure into eating sugary, fatty junk food.
Parents themselves are concerned about the sort of food their children eat.
A study of the diets of primary schoolchildren, published last year, revealed that children's intake of carbohydrates, fibre and iron were too low when compared with Government guidelines, while their consumption of sugar and fat was too high.
Today's report, by the market analyst Mintel, says that more than a third of mothers of children under 16 think that there is too much sugar in children's food, and two-fifths are concerned about fat levels. Almost half believe that many products aimed at children have too many artificial ingredients.
At the same time, forcing children to eat a nutritious diet is an uphill struggle. Almost one in five parents claim that their offspring will not eat any fresh vegetables and more than two in five claim that they are fighting a constant battle to cut down on the amount of crisps, cakes and sweets in their children's diet.
Colin Spencer, president of the Guild of Food Writers, said: "We live in the first society historically where children choose their diet. Before, children always ate what they were told. There is a tremendous amount of commercial pressure."
Mr Spencer called on the Government to regulate advertising for children and make more effort to promote healthy eating: "It is pretty disastrous that there is so much advertising directed towards kids, and the government ought to stop it," he maintained
He said there was a particular problem in Britain: "In France, children eat what their parents do far more readily. The problem is, there is no tradition of good food in Britain as there is in France. There is a great cultural tradition which we are lacking."
Liz Bannerman, a mother of two, said that she tried to give her seven- year-old and four-year-old a healthy diet, particularly a traditional Sunday lunch, and banned trips to fast food joints.
But she said it was impossible to do that all the time: "If your children are pestering you for junk food, it depends how tired you are. If it's the end of the day, you give in. If there are friends around, you give in very quickly. As a last resort, it's whatever you can get down them."
The children's food market is a huge one - and one which can afford to spend a lot of money on advertising. Mintel considered seven different types of food: pizzas, beefburgers, bite-sized chicken, fish fingers, chips, baked beans and canned pasta.
Between them these foods accounted for a total market worth some pounds 1.1bn, and manufacturers are forecast to spend pounds 15.2m on advertising the products to children this year - double the amount spent five years ago.
The companies often used tie-ins with familiar characters, such as HP's canned pasta ranges with Mighty Morphin' Power Rangers, or Buxted's Batarang Nuggets - bat-shaped nuggets of turkey.
For two years, in an Easter- egg promotion run for Cadbury's, packs of oven chips included vouchers offering 75p off chocolate eggs.
Last year a report by the National Food Alliance found that children saw three to four times more advertising for fatty and sugary foods than adults. The paper, Easy to Swallow, Hard to Stomach, found that seven out of 10 advertisements shown during children's programmes were for food, compared with two out of 10 during adult viewing.
Though Government guidelines for a healthy, balanced diet recommend that fatty and sugary foods should account for no more than 7 per cent of our diet, the survey found advertising for these foods made up 44 to 76 per cent of all food advertising.
Out of 549 food adverts monitored, only two were for fruit and vegetables, though it is recommended these should make up 33 per cent of a healthy diet.
Emma Besrode, Mintel's research manager, argued that it could make good financial sense for the food manufacturers to cater to parents' desire for healthy foods.
"Given the importance of the healthy message in relation to children's food, it is surprising that so little has been done by manufacturers to assist parents in the preparation and planning of easy but healthy children's meals," she said.
"There has been little in the way of recipe ideas or nutritional information, which tends on packs to be limited to standard nutritional content."
What children most like to eat
No of mothers interviewed 6,613 6,663
Baked beans 98 97.1
Frozen chips and 74.2 82.5
Frozen fish fingers 84.8 81.2
Frozen beefburgers 78.4 77.3
Tinned pasta 73.7 73.1
Frozen pizzas 71.3 63.9
Source: BMRB, TGI 1991-95/MintelReuse content