Jeremy Hunt’s key argument in his demands for a seven-day service in NHS hospitals has been called into question by his own department, in a leaked report which says it is not able to prove that fuller staffing would lower the numbers of weekend-admitted patients dying.

The report also admits it will be “challenging” to meet the government’s promise to recruit 5,000 more GPs by 2020, a Conservative pledge during the election campaign, and that 11,000 new staff will be needed to run a seven-day service in hospitals.

The increased numbers of deaths among patients admitted at weekends has been the cornerstone for Hunt’s argument in favour of a seven-day health service, with the health secretary citing 15 international studies since 2010, including one co-authored by the NHS’s top doctor Prof Sir Bruce Keogh, which indicate an increase of deaths in hospitals at the weekend.

However, an internal Department of Health draft report, leaked to the Guardian, says the department “cannot evidence the mechanism by which increased consultant presence and diagnostic tests at weekends will translate into lower mortality and reduced length of stay”.

Critics have long argued Hunt’s figures are skewed and that patients who attend hospital at weekends are far likely to be sicker or unable to access alternative palliative care services.

Hunt threatened last July to impose a new contract on consultants to help bring about the seven-day NHS, if they did not resume negotiations. The tactic worked and negotiations restarted in September. Talks were said to be going well, but the junior doctors’ dispute, in which Hunt has vowed to impose a new contract, has complicated matters and delayed final agreement being reached.

When the Guardian interviewed Hunt last Friday, he refused to rule out imposing a contract on consultants in England if they did not agree to work at weekends as part of their normal duties, as part of his push to honour the Conservatives’ manifesto pledge to create a “truly seven-day NHS” by 2020.

Keogh’s September 2015 report for the British Medical Journal found that 11,000 more patients a year die within 30 days of going into hospital if they are admitted for treatment between Friday and Monday, but he said it was “not possible to ascertain the extent to which these excess deaths may be preventable; to assume that they are avoidable would be rash and misleading”.

Consultants currently have a contractual right to refuse non emergency work at weekends or in the evenings, though the majority still do so. In the leaked report from mid-January titled “Seven-day NHS – update on progress and plans”, the department warns:

• Community and social services could not cope with more discharges at weekends.

• More than 11,000 new staff are needed at weekends at hospitals in England if they are to function identically to a weekday, including 3,000 nurses and 4,000 doctors.

• The seven-day plan is likely to have an additional cost of £900m each year.

Other challenges include recruiting the numbers of doctors and other staff needed for seven-day services, and “engaging consultants and junior doctors in the need for change”.

Dr Mark Porter, the British Medical Association’s chair of council, said: “This leaked document makes clear that more seven-day services will require not only thousands of extra doctors, nurses and support staff but an additional investment in both the NHS and community care.

“Its findings also show no proven link between weekend mortality rates and consultant presence, and suggests that other investment is more necessary.”

A Department of Health spokesperson said: “There is clear, independent clinical evidence of variation in the quality of care across the week and, working together with the NHS, we are determined to tackle this problem. Making sure the right staff and support is available for all patients seven days a week is a key part of our approach.”

The BMA and the Royal College of GPs (RCGP) have historically expressed sharp scepticism at the government’s pledge to recruit 5,000 more GPs, a promise reiterated by David Cameron in his election victory speech on 8 May and which the Department of Health says it is still committed to.

NHS England expresses the same concern in the leaked draft report: “The commitment to seven-day GP access is … dependent on the commitment to an additional 5,000 GPs working in general practice, which is a challenging target, both in terms of recruitment and retaining the existing workforce.”

Porter said the document “echoes the BMA’s concerns around the government’s recruitment target for GPs, at a time when one in three GPs are considering retiring in the next five years and hundreds of GP trainee posts were left vacant this year. If the government is to continue with its plans for extra seven-day services, it owes it to patients to convincingly explain how it will finance and staff it”.

Dr Maureen Baker, chair of the RCGP, said the pledge for 5,000 extra GPs was an ambitious target but necessary in an era when family doctors are performing 60m more consultations than five years ago. “It is a pledge that has been made and hard-working GPs across the country who are struggling to cope with unprecedented patient demand, and our patients, are counting on it,” she said.

“Many are leaving the profession to work elsewhere, or choosing to retire early, and there are currently not enough medical graduates becoming GPs to replace them. We fear that the secretary of state’s decision to impose the contract on junior doctors will only exacerbate this situation.”

The report says that seven-day care may not bring about the faster discharges of patients that the NHS has identified as vital to making the £22bn of efficiency savings it has committed to by 2020, warning that “community and social services [are] not sufficiently in place to support more discharges at weekends”.

Doctors have often argued that it is a lack of available community care, rather than a lack of hospital staff, which keeps patients in hospital longer than they should be.

The report reveals how many staff the government estimates it will need to recruit to cover the seven-day NHS – about 11,000 new staff are needed, including 1,600 consultants, 1,500 registrars and 900 junior doctors.

Senior medical professionals have been warning of a recruitment crisis in the profession, worsened by critically-low morale after Hunt vowed last week to impose a new contact on junior doctors by August.

NHS England’s report says the “additional number of staff required has been calculated by increasing the number of staff at the weekend … in order to match weekdays”.

In 2015, NHS England commissioned Deloitte to produce a report exploring the additional cost of a seven-day NHS service in hospitals. There has not yet been a public account of the findings, but the leaked Department of Health update states that Deloitte found there would be an additional annual net cost of £900m, after “benefits such as reduced length of stay and reduction admissions”. The figure is “the most robust estimate we have,” the report says.

• This article was amended on 16 February 2016. An earlier version said incorrectly that “consultants currently have a contractual right to refuse to work at weekends or in the evenings, though the majority still do so”. Consultants currently only have the right to refuse non-emergency work.