Labour has accused Boris Johnson of misleading the public when he promised to recruit 20,000 police officers after it emerged from leaked correspondence that thousands are likely to be recruited away from frontline roles.

The opposition has seized on a letter written by the home secretary, Priti Patel, to the London mayor, Sadiq Khan, last week, in which she says the new officers will be allocated “between territorial, regional and national policing functions”.

Sources suggest this could mean as many as 7,000 of the 20,000 officers could be allocated to bodies such as the National Crime Agency, leaving territorial forces in England and Wales with fewer recruits than expected.

The Met fears that its allocation would be 2,000 officers down – the force had hoped to recruit 5,000 officers on the back of Johnson’s promise, one of the first he made after entering No 10 last month.

The meaning of the pledge is almost certain to be raised at a meeting between Patel and Khan that is likely to be tense. It is expected to take place on Wednesday, the first formal meeting between the two since the home secretary was appointed.

Louise Haigh, the shadow policing minister, said the letter “clearly shows that Boris Johnson’s grandiose pledge of 20,000 more frontline police officers was absolutely nothing of the sort”.

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She said: “A huge proportion of the new recruits won’t be in the frontline and people simply won’t be seeing the extra police officers on the streets that they were promised.”

Sources said police forces had petitioned the Home Office for extra numbers, with the National Crime Agency and other national forces requesting between 6,000 and 7,000 in total. That would reduce the number available to the Met and other territorial forces to around 13,000.

A Home Office source said: “It’s sad to see Sadiq Khan is once again more focussed on playing politics and leaking the contents of letters to the media than backing the government’s drive to recruit the police officers he claims to want.”

Police sources also expressed surprise at Khan’s positioning, saying the Met had asked him to bid for more officers than he ultimately asked for. “We asked the mayor to request 5,500 extra officers for the Met, but he only asked for 5,000.”

Johnson implied the new recruits would be “bobbies on the beat” when he confirmed he would act on a pledge seen as critical in fending off criticism from Labour over declining police numbers.

The prime minister said: “People want to see more officers in their neighbourhoods, protecting the public and cutting crime” and added: “I promised 20,000 extra officers and that recruitment will now start in earnest.”

Police officer numbers have declined every year since the Conservatives returned to government in 2010, with the total number of officers in England and Wales down by 20,564 between March 2010 and March 2019.

Before the meeting with Khan, Patel sent a four-page letter setting out her initial thoughts on how the two might work together.

The home secretary acknowledged the prime minister’s commitment to recruiting an additional 20,000 police officers.

She added:“I am regularly in discussions with policing leaders, including in London the commissioner of the Metropolitan police service, Cressida Dick, on the allocation of these officers between territorial, regional and national policing functions.”

A Home Office spokesperson indicated that the final allocation of extra officers to police forces would include the National Crime Agency, which tackles serious and organised crime. “We have been clear we will work with the police to consider how best to allocate the 20,000 to ensure we protect the public, serve communities and tackle current and emerging threats, including serious and organised crime and serious violence,” said the spokesperson.