The chancellor has been accused of exaggerating an increase in the amount of funding for counter-terrorism policing, after a leaked letter from a security official said the year-on-year rise was £59m rather than the £160m announced in the budget.

Philip Hammond, whose budget speech included an announcement of extra funds for counter-terrorism, said on Monday: “We committed in 2015 to spend 30% more on counter-terrorism capabilities over the current spending review period. And today I commit an additional £160m of CT [counter-terrorism] police funding in 2019-20 to protect CT police numbers and to allow future CT police funding to be considered in the round at the spending review.”

But a letter, seen by the Guardian, from a senior official from the Office for Security and Counter Terrorism, part of the Home Office, said next year’s extra funding only amounted to £59m. It said: “It represents a £59m year-on-year increase in CT police funding.” It was sent on Monday to the chair of the counter-terrorism policing strategic board.

The letter was written by the head of the OSCT’s capabilities, operations, policing and secretariat unit, whom the Guardian was asked not to name for security reasons.

Government officials confirmed that the letter was genuine – while Treasury officials said the chancellor was correct to use the £160m figure when he addressed MPs in the Commons.

Hammond’s speech on Monday made no mention of the £59m figure, and neither did the home secretary, Sajid Javid, speak of it. Javid addressed a conference of police chiefs on Wednesday citing “the increase in funding for counter-terrorism policing for 2019-20, an increase of £160m”.

The government has been under pressure to increase police funding and has also been proclaiming that austerity in the UK is over.

A spokesperson for the Treasury said Hammond had been correct about the amount of money he had announced on Monday in the budget speech: “£160m of additional funding is entirely the correct way to describe the counter-terrorism budget announcement.”

The Treasury said the £160m figure was correct because it was the difference between the annual amount given in the 2015 spending review settlement (£656m) and the funding granted to counter-terrorism policing for 2019/20 (£816m).

But this year’s funding was boosted by an extra top-up from elsewhere, taking the actual total for the year to £757m. That extra funding was not included in the chancellor’s calculation.

Labour’s policing spokesperson, Louise Haigh, said: “The government have been caught being misleading time and time again on police funding. They’ve slashed budgets for eight years at the expense of public safety and now they’ve been caught red-handed once again massively exaggerating the amount that is actually going into counter-terrorism policing this year. The public and the police deserve better.”