Theresa May has been officially rebuked for misleading MPs and the public over false claims that the government is providing an extra £450m in funding to local police forces in 2018/19.

The chair of the UK Statistics Authority, Sir David Norgrove, ruled on Tuesday that the claim made by May repeatedly at prime minister’s questions last month “could have led the public to conclude incorrectly” that the government was providing an extra £450m for police spending over the next financial year.

Labour MPs are expected to try to challenge May over her misleading statements about police funding at prime minister’s questions on Wednesday.

The shadow police and crime minister, Louise Haigh, who made the complaint to the statistics watchdog, said that in fact there had been a “flat cash” settlement for police forces in England and Wales that actually amounted to a cut in direct Whitehall grants to the police in real terms. Haigh said the “extra £450m” would only be found if police and crime commissioners pushed through an increase to council tax to raise £270m. About £130m of the £450m is to go directly to “national police priorities” rather than local forces and a further £50m is to be provided for counter-terrorism funding.

The prime minister’s claim that local police force budgets were being boosted by £450m was repeated by Home Office tweets and in a letter sent out by Andrea Leadsom, the leader of the House of Commons.

“We have commented in the past about statements on police funding and emphasised the need for greater precision in the way numbers are used,” Norgrove told Haigh in his response to her complaint.

“In terms of the particular points you make, the prime minister’s statement and the Home Office’s tweet could have led the public to conclude incorrectly that central government is providing an additional £450m for police spending in 2018/19.

“The Home Office tweet also implied that the £450m sum is guaranteed. As the minister for policing’s statement outlined, up to £270m of the funding settlement will come from local council tax, if police and crime commissioners and mayors choose to raise these sums. In addition, the leader of the House of Commons stated that the £270m that can be raised locally was on top of the overall settlement of up to £450m,” wrote Norgrove.

The statistics watchdog said complex funding arrangements were difficult to explain in the “time compressed context” of PMQs but said the Home Office did not face this constraint in its tweet. He suggested the Home Office’s head of statistics made sure his colleagues understood the structure of police funding and the importance of making clear public statements.

Haigh called for the PM to apologise. She said: “The Tories are not being straight with the public on police funding and now they have been found out.

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“You would hope this embarrassing slapdown would now shame the Conservatives into being honest about their dismal record on policing. With 21,000 officers gone and billions cut in real terms, it’s time the government stopped taking the public for fools.

“The prime minister should apologise for trying to pull the wool over people’s eyes on Tory cuts to policing.”

The Home Office said: “The police funding settlement for 2018/19 that we set out delivers an increase in overall police funding. We aim to be as clear as possible in communicating it to the public and have repeatedly said that around £270m of the up to £450m increase in police funding next year results from increased council tax precept income, which is dependant on police and crime commissioners’ decisions. Since the funding settlement, almost all police and crime commissioners have decided to use this flexibility to raise extra precept income.”