The research was based on a public consultation in which Ofcom presented three regulatory options.
Consumers rejected timing restrictions on all food and drink because such a move would penalise ads for "healthy" food.
They opted for restricting ads only for foods high in fat, salt and sugar, and at periods when the largest numbers of children were watching TV - yet without going as far as a pre-9pm watershed ban. The option based on volume restrictions was rejected.
The results of the consultation are due to be published shortly.