The body representing Britain's chief police officers is facing a worsening rebellion from police authorities as the scale of the funding issue and some of the reasons behind decisions emerge.

Up to 13 of the 43 police authorities in England and Wales will, for the first time this year, refuse to pay money to the Association of Chief Police Officers (ACPO), according to sources on both sides, because they accuse the body of lacking accountability and remaining too large while the rest of the police service is undergoing cuts.

The Home Secretary, Theresa May, has been made aware of the funding boycott – the latest controversy to embroil ACPO – but will not intervene.

Already the police authorities which fund the Kent and Hampshire forces have refused to pay their ACPO subscriptions.

One of Britain's largest forces, Merseyside, said that, so far, its budget contained "no provision to make ACPO subscriptions"; the Staffordshire police authority votes on the issue on Wednesday ; the Metropolitan police authority said its payment of £195,000, the largest single contribution, was still under consideration; and West Midlands is also still to commit to paying its subscriptions.

ACPO's last accounts show an operating deficit of £423,000. Its supporters say the withholding of money would be "dysfunctional and destabilising".

The ACPO president, Sir Hugh Orde, tried to head off criticism over the undercover units the body used to run. His call for radical reform comes after revelations of seven-year spying missions against environmental protesters, with undercover officers revealed to have been so poorly supervised that some of them slept with activists.

Orde said he wanted senior officers stripped of the sole power to authorise the use of undercover officers and called for judges to approve the intrusive tactic.

It follows revelations about undercover officer Mark Kennedy and the dropping of charges against six protesters accused of planning to invade Ratcliffe-on-Soar power station in Nottinghamshire. Police face allegations they suppressed evidence of Kennedy's undercover work which would have exonerated the six defendants.

Sources with knowledge of the funding row surrounding ACPO say some Police Authorities have cited annoyance at ACPO's alleged aloofness and lack of accountability, while others feel it will remain too big despite the cuts being faced by the rest of the police service.

Money to fund ACPO is paid on behalf of police forces by their police authorities, which hold their budgets. Police Authorities pay a total of £830,000 a year to fund ACPO's central secretariat staff of 29, with the Home Office paying about the same amount.

The Association of Police Authorities (APA) said individual members would be left to decide whether to fund ACPO's secretariat, in effect its central London headquarters and policy work.

Critics point to the fact the other national policing bodies, such as APA, have cut staff by up to 50%, while ACPO is not planning reductions.

Individual police forces are expected to continue funding direct police work, such as ballistic experts services which ACPO supplies to all constabularies.

One senior source with knowledge of the discussions said: "There is anger at ACPO for not cutting and over accountability. What exactly do they do? People are asking why they should be paid for their administration."

One senior ACPO source accepted its image had been damaged by issues such as the fact that the organisation is a limited company.

Orde has repeatedly said he would make the body more accountable and has been waiting for the government to approve or amend his plans to turn the body into a chartered institute for policing.

The APA said: "The sum total of individual police authorities' financial support to the cost of ACPO's central administration was about £830,000 last year. This financial support was in addition to authorities' considerable contributions in the form of their wholehearted support for their chief officers' work with ACPO at a national level.

"This position reflects the fact that, in the context of the extraordinary pressure of front loaded cuts to policing budgets, individual authorities' decisions on all financial commitments would be especially difficult. Therefore this year, perhaps more than ever, it is right that difficult decisions on funding are made at a local level where local taxpayers can hold those taking those decisions to account.

"The APA values ACPO as an important partner in the tripartite governance of policing, whilst maintaining our longstanding call for it to be reformed and made more accountable to the public."

A Home Office spokesperson said: "The Home Secretary was made aware by the APA of the emerging position on police authority funding for ACPO, but it is for individual Police Authorities to decide whether to continue to provide this support.

"We see ACPO as an important part of the policing landscape, and we are working with them on their long-term funding and how they could strengthen their professional leadership of the police service."