The sugar tax applied to fizzy drinks could be extended to pre-packaged milkshakes and lattes under new government plans.
The government is consulting on proposals to end the exemption from the tax for milk-based drinks, as well as non-dairy substitutes such as oats or rice.
Chancellor Rachel Reeves announced in her autumn budget last year that the government was considering widening the levy.
Shadow chancellor Mel Stride labelled the move a "sucker punch" to households when Labour had "already pushed up the cost of living for families".
The sugar tax, known formally as the soft drinks industry levy (SDIL), is a tax on pre-packaged drinks such as those sold in cans and cartons in supermarkets.
It applies to manufacturers and was introduced by the Conservative government in April 2018 as a means to tackle obesity.
On Monday, the Treasury also confirmed proposals to reduce the maximum amount of sugar allowed in drinks before they become subject to the levy from 5g to 4g per 100ml.
Some 203 pre-packed milk-based drinks on the market, which make up 93% of sales within the category, will be hit with the tax unless their sugar content is reduced in accordance with the proposals, government analysis says.
Home Secretary Yvette Cooper said the government was consulting on "going further" with the existing levy after it was shown to have had a particular impact on children's health.
"We are making sure we are taking practical, sensible measures to improve the health of our children," she told BBC Breakfast on Tuesday.
The original exemption for milk-based drinks was included because of concerns about calcium consumption, particularly among children.
Announcing the planned changes, the Treasury said young people only get 3.5% of their calcium intake from such drinks, meaning "it is also likely that the health benefits do not justify the harms from excess sugar".
"By bringing milk-based drinks and milk substitute drinks into the SDIL, the government would introduce a tax incentive for manufacturers of these drinks to build on existing progress and further reduce sugar in their recipes," it added.
The government estimates that 89% of soft drinks sold in the UK are not subject to the tax because of widespread reformulation by manufacturers since 2018.
But it added that the levy had effectively created a "target" of just below the 5g threshold, and products had clustered below 5g as a result.
The government consultation will run from Monday until 21 July.
