News that the UK economy grew faster than expected in the first three months of this year is also expected heap further pressure on the prime minister and the chancellor.
Mr Sunak has said he would like to cut taxes in the future, but that he had to be prudent given the state of the economy.
The chancellor Jeremy Hunt is resisting renewed calls for immediate tax cuts.
Treasury minister Andrew Griffith said they were "not for the moment" when asked about the prospect of cuts, warning of the need to reduce inflation.
His comments came after a report said that since 2019 the UK has seen the biggest set of tax rises since the war.
By the time of the next general election, taxes are likely to have risen to around 37 per cent of national income, according to analysis by the highly respected Institute for Fiscal Studies (IFS).
The spike was equivalent to around £3,500 more per household, even if it will not be shared equally, it warned.
Former cabinet minister Dame Priti Patel told GB News: "The tax burden is now at a 70-year high. That is unsustainable. And the people that pay the taxes are hard-pressed Brits around the country.
"As Conservatives, we believe in lower taxes. As Conservatives, we believe being on the side of hard-working households and families. As Conservatives, we believe in hope and aspiration.
"That should mean lower taxes. The burden of tax has to start to come down.
"Reduce the size of the state and ensure that people keep more of their income. This is just a fundamental Conservative principle that we must stand by."
She also said there was a need to "separate" tax and inflation, adding: "I do recall a rather successful Conservative prime minister, Margaret Thatcher, was able to tackle inflation while growing the economy."
Former prime minister Liz Truss said the “unprecedentedly high tax burden” was “one of the reasons that the British economy is stagnating and why we need to cut taxes to help make Britain grow again”.
On tax cuts Mr Griffith told Times Radio: "Look, I don't think any responsible Treasury minister is going to give you that commitment.
"I can point to what the proud track record of Conservative governments are, the fact that philosophically we believe that you need a strong economy, you need to build that on stable foundations, which is why bearing down on inflation is so important, that's been the priority the Prime Minister has set.
"We're on track to deliver that because of the tough choices we've made. Directionally Conservatives believe in people keeping more of their own money, but I regret I can't give you a commitment at seven o'clock outside of a fiscal event as to the specifics of that.
"But it's clearly something that's a consequence of that really significant extra amount of money, no-one planned for, no-one foresaw, due to the global pandemic."
Asked when tax cuts will be announced, Mr Griffith told LBC: "Not for the moment, I'm afraid, because you've got to make choices.
Ben Zaranko, from the IFS, said the pandemic could not be blamed for rising tax levels, predicting a high-tax approach would remain regardless of which party is in power.