The calls for more stringent regulation were made in a report from the health select committee examining how the UK can better tackle childhood obesity.
While the committee was positive about the Committee on Advertising Practice’s new rules banning the advertising of unhealthy food and drink products in children’s media, it said the regulator "could — and should — go further".
It added: "We urge a re-examination of the case for further restrictions on advertising of HFSS (high in fat, salt and sugar) food and drink in the light of the most recent research not only on the effect of such advertising, but on the scale and consequences of childhood obesity."
Regarding in-store promotions, the committee said that it was "extremely disappointed that the government has not regulated to provide the ‘level playing field’ on discounting and price promotions, which industry representatives themselves have told us is necessary for the greatest progress".
It called on the government to seek advice from their public health advisers and regulate "to further reduce the impact of deep discounting and price promotions", while adding that it welcomed some of the actions retailers have been taking to direct promotions away from foods and drink high in sugar, salt and fat.
In response, health minister Nicola Blackwood said: "We welcome the committee's recognition of the progress we have made in this area, delivering the most ambitious plan on childhood obesity in the world."
"It is backed by the soft drinks industry levy as well as the most comprehensive reformulation programme of its kind, anywhere.
"Voluntary approaches have been shown to be very effective, but as we have repeatedly said, we have not ruled out further measures if results are not seen."
But in the report, committee chairwoman Dr Sarah Wollaston was dismissive of "vague statements about looking ‘to further levers’ if the current plan does not work", adding that they "are not adequate to the seriousness and urgency of this major public health challenge".