Mr Hunt has dealt with conservatives on the right, saying tax cuts were 'virtually impossible' at the looming autumn budget.
A surprise fall in inflation in August and government borrowing coming in lower than anticipated had raised Tory hopes that Mr Hunt would be able to offer tax cuts in November.
But the chancellor has still had some 'frankly very difficult decisions' as he pushes on with stringent measures to balance the books and help bring down inflation.
The former Tory PM Liz Truss is among those on the Tory right demanding that Rishi Sunak and his chancellor bring down the tax burden at an autumn statement on 22 November.
Mr Hunt said there was no extra headroom to cut taxes, as he prioritises Rishi Sunak's promise to halve inflation this year to a level of around 5.3 per cent.
Pleading for patience from Tories on the right, the chancellor added: ''T, it makes life extremely difficult - it makes tax cuts virtually impossible and it means that I will have another set of frankly very difficult decisions.
The Bank of England's holding of interest rates for the first time in nearly two years, leaving them unchanged at 5.25 per cent on Thursday, meant no added value to the cost of national borrowing.
A surprise fall in inflation to 6.7 percent in August and government borrowing coming in less than official forecasts that month had also shifted expectations.
Low-tax Tory MPs have been pushing for income tax cuts. But it looks as if they may have to wait until the Spring budget - when the government is expected to try to find headroom for tax cuts ahead of the general election.
The chancellor is reportedly considering making real-term cuts to benefits at the autumn statement. The government has been warned that failing to hike benefits with inflation would be a disaster for hard-pressed families.
The three politicians are also said to be mulling a 'tweak' to the triple lock to limit costs, meaning pensioners may not receive a bumper 8.5 per cent increase in the state pension, with an increase of around 7.8 per cent instead.
The Bank of England is 'probably done' with interest rate increases, with 5.25 per cent now expected to hold as the base rate for an extended period, said Samuel Tombs, an economist at Pantheon Macroeconomics.
The property market responded to the news with relief. Riz Malik, the chief executive of mortgage broker R3 Mortgages, said: ''I don't think we can make mistakes with the mortgage market.