The governor of the Bank of England has dismissed concerns raised by the Conservatives that the new government’s plans for public sector pay rises would risk stoking inflation and keep interest rates higher for longer.

After the Bank cut the cost of borrowing for the first time since March 2020, senior Tories including Rishi Sunak and Jeremy Hunt said above-inflation salary increases for teachers, nurses and other public sector workers could delay further rate reductions.

Seizing on the Bank’s decision as evidence that Labour had “inherited a strong economy” from the previous government, the former prime minister wrote on X: “My concern now is that Labour’s inflation-busting public sector pay rises have put further cuts at risk.”

However, the Bank’s governor, Andrew Bailey, told journalists after the rate announcement that the planned pay awards of 5-6% would have a relatively small impact on headline inflation, and suggested it was not a focus for the Bank.

He said the proposed pay increases would probably add less than 0.1 percentage points to headline inflation, relative to an expectation for a 2% pay deal which had been pencilled in by the previous government.

“The proverbial back of the envelope suggests an increment in the inflation space which is very small,” he said on Thursday. “I mean, you’re in quite small second decimal place numbers at that point.”

Sunak gambled his premiership on falling inflation and the central bank cutting interest rates when he announced the early general election, having argued that his administration had taken “difficult decisions” – including on public sector pay – in pursuit of this goal.

He had repeatedly argued that pay restraint was necessary to keep a lid on inflation, leading to bitter disputes with trade unions and rolling strikes amid warnings of a staffing crisis in the public sector.

However, the first reduction in borrowing costs since March 2020 did not ultimately arrive until a month after Keir Starmer defeated him with a landslide victory.

Darren Jones, the chief secretary to the Treasury, said: “After the Tories stoked interest rate rises with their reckless mini-budget, it’s astonishing that Rishi Sunak still thinks he is part of the solution, not the problem.”

In its first month in government, Labour has reached various agreements with unions, including a pay deal with junior doctors that could lead to their wages rising by 22.3% over two years.

The chancellor, Rachel Reeves, also announced this week that millions of public sector workers would get 5-6% pay increases for the current financial year, at a cost of almost £10bn, after accepting the recommendations made by public sector pay bodies.

Reeves announced the decision in a speech exposing a £22bn black hole that she accused the Tories of having “covered up” in the public finances, while seeking to plug the gap with cuts to winter fuel payments for 10 million wealthier pensioners, and hinting at tax rises in her first autumn budget.

Jeremy Hunt, the shadow chancellor, said on Thursday that the Bank “may now take longer” to deliver further interest rate cuts “because of inflation-busting public sector pay rises rushed through” by Reeves.

Mel Stride, who is standing to be the leader of the Conservatives, also reiterated the criticism, saying it was “important that Rachel Reeves’ stance on public sector pay doesn’t hinder further progress by feeding service sector inflation”.

Bailey, who in 2022 warned that workers asking for inflation-matching pay rises risked embedding high inflation for longer, said on Thursday the Bank would monitor closely developments in service sector prices and wage growth across the economy when considering any future rate cuts, but cautioned that it was likely to proceed slowly.

“We need to make sure inflation stays low, and be careful not to cut interest rates too quickly or by too much,” he said.

The central bank had been extensively briefed on Reeves’s announcement on Monday about public sector pay, he said, but that it would not include the changes within its forecasts for the economy until after the budget.

He suggested private sector wage developments would be more important for determining future rate cuts, and that they tended to “lead” the public sector, rather than the other way around.

Although saying that government decisions, including public sector pay, would have an impact on inflation, he stressed the need to take the announcements in the round.

“We’ll know a lot more about that when we have the budget. But you can do a sort of rough … calculation, and it isn’t that large actually.”