The tensions over economic policy and the timing of tax cuts are set to dominate debate ahead of the Budget on March 15.
Mr Sunk and Mr Hunt have both repeatedly said they want to cut taxes when they can, but argue the priority now must be bringing down inflation, which is at an annual rate of around 10pc.
Government figures continue to point to the implosion of Ms Truss’s tax-cutting “mini” Budget last autumn, which sent the pound sinking and interest rates soaring, leading to her ouster from Number 10.
Mr Hunt will reiterate that message in a speech designed to rebut calls for tax cuts in his March Budget and underscore the pressures on Treasury revenues.
A Treasury source told The Daily Telegraph: “The single biggest barrier to economic growth is 10pc inflation. You’re not going to grow the economy with inflation that high. It is the cause of industrial unrest, it is eroding the pound in people’s pockets and squeezing public services. You can have a thousand policies to promote growth, but without tackling inflation no one of them will work.”
Trying to ensure Northern Ireland can freely trade with the mainland UK while also avoiding physical checks on the border with Ireland has been one of the thorniest Brexit issues.
A customs border down the Irish Sea was effectively created when the UK signed the Northern Ireland Protocol, which set out the province’s terms of trade after Brexit.
Since then both Liz Truss and Mr Sunak have attempted to renegotiate that deal, with the UK threatening to unilaterally change the trade terms unless a new agreement is reached.
With pressure from Washington DC, Mr Sunak is hoping to agree a new deal by April, in time for the 25th anniversary of the Good Friday Agreement, which was a historic moment in the peace process.
Using different product labelling could theoretically ease the need for customs checks at the border. But Mr Norman argues in his letter that it would send costs soaring for producers.
At one point he warns: “A costly labelling solution will mean customers will be hit by reduced ranges, higher prices – at a time of huge inflation and when the economy in Northern Ireland is already disadvantaged – and a worsening of availability.”
At another he says: “This proposal adds cost, labour and complexity at a time when the supply base really does not need it and is struggling to stay on its feet to the specific advantage of EU producers.”
The exact labelling changes being proposed by London and Brussels is unclear, given talks remain behind closed doors – though some form of change has been floated in public.
Meanwhile the Treasury’s approach to tackling the twin challenges of lowering inflation and trying to minimise the recession forecasted for this year has faced recent criticism from senior businessmen.