Coca-cola has promised to stop advertising its drinks to children under 12.
Schemes to market the drinks to young children will be scrapped unless there is an educational or physical benefit.
It is also considering widening a Scottish trial, where it has removed branding for Coca-cola from vending machines in schools.
Teachers' representatives have welcomed the move.
Heinz has also said it will not target any advertising for its products solely at pre-school children.
However, it will continue to use pictures of TV characters on its packaging.
Obesity
There has been growing pressure on food and drink manufacturers to curb advertising to children.
They are blamed for contributing to increasing rates of obesity, especially in children.
Coca Cola own and operate a large number of vending machines, many of which feature photographs of its fizzy drinks on the front panel.
Under a trial in Scotland, photographs of the drinks were removed from the machines.
A spokesman said: "We don't sell our products through vending machines in primary schools but we do in secondary schools," said a spokesman.
"We need to look at the transition to non-branded fascia vending machines in Scotland to see if we should do it elsewhere."
It has widened a ban on advertising to the under-12s, which covered fizzy drinks, to include non-fizzy brands such as Oasis.
Doug McAvoy, general secretary of the National Union of Teachers (NUT), said: "These welcome moves by Coca Cola and Heinz are positive steps in the right direction.
"I call on the government to introduce regulations which ensure that all other food companies do the same.
"The NUT is committed to protect children and is concerned that schools are
increasingly under pressure to act as agents for food companies in ways that are
potentially damaging to children's health."
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