The Prime Minister said a consultation is to be launched which could also see all shops forced to apply the levy regardless of how small they are.
It emerged earlier this week that the Treasury had warned Number 10 that increasing the plastic bag charge from 5p “looks like profiteering” and should be avoided.
Mrs May said: “We have taken huge strides to improve the environment, and the charge on plastic bags in supermarkets and big retailers has demonstrated the difference we can achieve by making small changes to our everyday habits.
“I want to leave a greener, healthier environment for future generations, but with plastic in the sea still set to treble we know we need to do more to better protect our oceans and eliminate this harmful waste.”
The Prime Minister has already slapped down Mr Hammond over his warnings that a no-deal Brexit could cost the UK billions of pounds in lost revenue.
Speaking on a three-day visit to Africa this week, Mrs May said: “Look at what the director general of the World Trade Organisation has said,” she told reporters as she flew to Africa for a three-day trade visit.
“He has said about the no deal situation that it will not be a walk in the park, but it wouldn’t be the end of the world.”
She added: “What the Government is doing is putting in place the preparation such that if we are in that situation, we can make a success of it, just as we can make a success of a good deal.”