Prices are expected to go up over the next two years following last week’s £70 billion tax and borrowing bombshell.
It will also slow the decline in interest rates, the Bank said.
The stark warning comes as interest rates were cut to 4.75%, down from 5%.
But the Bank indicated that the process of reducing interest rates would be “gradual” from here, hinting another cut before Christmas is unlikely.
Shadow Chancellor Mel Stride said the cut will be welcomed by “millions of homeowners” and that it builds on the work the Conservatives did in office to hold inflation down.
“However, the independent OBR and the Bank of England set out that as a result of Labour’s choices in the Budget last week inflation will be higher,” he said.
“The Government must not undo the hard work the last government did.”
Inflation, which is now at 1.7%, plunged from more than 11.1% to 2% during Rishi Sunak’s final months as Prime Minister.
Announcing 0.25% interest rate cut the Bank’s Monetary Policy Committee Report found Ms Reeves’s budget will place upward pressure on prices.
Governor Andrew Bailey stressed that the underlying trend was “continued progress in disinflation”.
Speaking at a press conference, Mr Bailey admitted Britain faces both “greater global uncertainty” and “domestic uncertainties”.
He was quizzed about the potential impact of Donald Trump’s return as US president.
Asked about the possibility of Mr Trump sparking a global trade war when he returns to the White House in January, the Governor added: “We will have to watch this very closely.”
But Mr Bailey warned it was “not useful or wise to enter into speculation” about what economic policies Mr Trump might pursue, including proposed higher tariffs on US imports.
Ms Reeves said the interest rate cut would be “welcome news” for millions of families, but added that households are still facing a challenge after Liz Truss’ mini-budget.
“Today’s interest rate cut will be welcome news for millions of families, but I am under no illusion about the scale of the challenge facing households after the previous government’s mini-budget,” the Chancellor said.
“This Government’s first Budget has set out how we are taking the long-term decisions to fix the foundations to deliver change by investing in the NHS and rebuilding Britain, while ensuring working people don’t face higher taxes in their payslips.”
