Children largely inherit their taste for high-protein food like meat and fish, research suggests.
Children often follow their parents' example
However, Cancer Research UK found a liking for vegetables and puddings was less likely to be fixed, and more the result of the menu provided by parents.
The Journal of Physiology and Behaviour study also found girls were more likely to enjoy vegetables than boys.
The researchers based their conclusions on a study of more than 200 pairs of same-sex twins.
About half were identical twins, and the rest were non-identical.
Identical twins share all their genes, and so comparing their food preferences with those of non-identical twins - who share about half their genes - highlights the difference between what is inherited and what is influenced by environment.
Mothers of children aged between four and five were given a list of 77 foods.
Lead researcher Professor Jane Wardle, of Cancer Research UK's health behaviour unit, said it was not clear why environmental factors were more influential in determining preferences for fruit, vegetables and puddings.
She said it might be down to the greater variety of choice available in these categories - unlike in meat or fish.
"It might be that children who witness their parents show enthusiasm or distaste for certain types of vegetables or puddings are likely to follow suit.
"Or it might be that if a particular food is always available children learn to like it.
"For instance, if a fruit bowl is always full of bananas children might think of them as being a favourite food."
Professor Wardle said the findings suggested that parents could have a profound impact on their children's dietary preferences - and steering them towards healthy options could set a blueprint for life.
"Finding out more about why children like and dislike foods is important in helping us understand the problems of obesity.
"Childhood obesity can lead to a number of health problems in later life including cancer."
Dr Lesley Walker, director of cancer information at Cancer Research UK, said: "This study is important because it adds to our knowledge of understanding very young children's food preferences.
"The more we know about this the better we can understand what leads to bad eating habits which bring with them a whole range of health problems including cancer."