Liam Fox has said it would be unthinkable not to spend some of the “Brexit dividend” from leaving the EU on funding the NHS, but the government could not make any promises at this point.

The pro-Brexit trade secretary waded into the debate after Boris Johnson, the foreign secretary, infuriated colleagues by having his allies brief that he wanted £100m a week from EU spending to be set aside for funding healthcare.

At least eight members of the cabinet intervened to reprimand Johnson for letting his position be known before confidential cabinet discussions on the NHS.

Amber Rudd, the home secretary, stressed the importance of trust between cabinet members, according to one person present. “I’m talking to you, foreign secretary,” she reportedly said.

However, Johnson appears to have successfully put the issue on the national agenda, with ministers repeatedly pressed about whether the government will give some of the money saved from leaving the EU to the NHS.

Fox told BBC Radio 4’s Today programme he supported giving more money to the NHS and healthcare would always be a priority, but the government could not set out how any money from Brexit would be spent after the UK’s proposed transition period ends in 2021.

“Once we have left the EU, once we have completed any implementation period that requires contributions to the EU, yes, we have control over more of the money and the government at the time will be able to determine how we spend the money on the priorities the British people have at that point,” he said.

“But I completely agree, not least as a GP myself, that spending more money on healthcare has to be a good thing for the UK

… I find it absolutely unthinkable that health would not be among the top of [the priorities].”

Fox refused to be drawn into the spat over Johnson, but acknowledged: “I think it’s very useful to remind people that we will get a dividend from leaving the EU.”

Other cabinet members are less convinced there will be huge sums to spend on public services after leaving the EU, which they believe will cause other financial pressures.

Meanwhile, the chancellor, Philip Hammond, made clear that Johnson was the foreign secretary, not someone involved in health policy.

“I gave the health secretary [Jeremy Hunt] an extra £6bn in the recent budget and we will look at departmental allocations again at the spending review when that takes place,” he said.