The government is set to offer around 1 million NHS staff a 6.5% pay rise over the next three years but is insisting that health workers give up a day’s holiday in return for the £3.3bn deal.

Ministers hope they are close to finalising a package to give NHS personnel in England their first meaningful pay rise since 2010, after months of behind-the-scenes talks with union leaders.

The Treasury and Department of Health and Social Care plan to propose that all non-medical NHS staff in England receive a 3% increase in their salary in 2018-19 – the current rate of inflation – and then rises of 1%-2% in the following two years. Nurses, midwives, healthcare assistants, ambulance staff and all other workers except doctors and dentists would benefit from the scrapping of the hated pay cap. Doctors and dentists have a separate pay review system.

The deal the government is preparing to formally put to staff later this month would also see some NHS personnel get pay rises of 10% and, in certain circumstances, well above that by 2021. Those on the bottom of the NHS’s nine pay scales would get a bigger uplift under Agenda for Change – the agreement that governs the earnings of health service staff – than colleagues who earn more because they are higher up that pay band.

The 14 health unions that have been negotiating the details of the government’s offer, in conditions of strict secrecy, are cautiously optimistic they will feel able to recommend it and that their members, who include Unison, Royal College of Nursing, Unite, the GMB and Chartered Society of Physiotherapists, will endorse it.

Sources close to the talks say they have been constructive, businesslike and highly detailed, with both sides keen to see NHS staff pay improved as much as possible. A plan for the chancellor Philip Hammond to unveil the offer in his Spring Statement next Tuesday has been abandoned, however, as there are still some sticking points to be resolved.

Ministers’ determination that staff forfeit a day’s holiday in return for the pay rise could derail the chances of the Treasury and unions agreeing a deal, especially if that provokes a backlash among staff, many of whom already do regular unpaid overtime and have seen their real incomes cut by up to 14% by the years of austerity-era tiny rises.

But government negotiators have made clear that staff working one extra day a year is a “red line” that for them is non-negotiable. If union members refuse to accept that, ministers will withdraw their offer in its entirety and may impose the 1% pay rise that was planned before anger at eight years of zero and 1% public sector pay rises proved so politically damaging for the Conservatives in last year’s general election campaign.

Q&A Does the UK have enough doctors and nurses? Show The UK has fewer doctors and nurses than many other comparable countries both in Europe and worldwide. According to the Organisation for Economic Co-operation and Development (OECD), Britain comes 24th in a league table of 34 member countries in terms of the number of doctors per capita. Greece, Austria and Norway have the most; the three countries with the fewest are Turkey, Chile and Mexico. Jeremy Hunt, the health secretary, regularly points out that the NHS in England has more doctors and nurses than when the Conservatives came to power in 2010. That is true, although there are now fewer district nurses, mental health nurses and other types of health professionals. NHS unions and health thinktanks point out that rises in NHS staff’s workloads have outstripped the increases in overall staff numbers. Hospital bosses say understaffing is now their number one problem, even ahead of lack of money and pressure to meet exacting NHS-wide performance targets. Hunt has recently acknowledged that, and Health Education England, the NHS’s staffing and training agency, last month published a workforce strategy intended to tackle the problem. Read a full Q&A on the NHS winter crisis

The issue of NHS pay twice left Theresa May looking out of touch when she was quizzed on it live on television. On BBC1’s The Andrew Marr Show, she said there were “many complex reasons” why people went to foodbanks when asked why some nurses were doing that. And she first insisted that “there’s no magic money tree” when confronted by an NHS nurse, only to find a £1bn “bribe” to win the support of Democratic Unionist party MPs in key votes when her government lost its parliamentary majority.

The unions may be helped in selling the package to their members by ministers agreeing not to change their system of pay increments. Also known as “progression pay”, this gives about half of staff 3% or 4% annual rises on top of their annual increase. Jeremy Hunt, the health and social care secretary, had signalled last autumn that it may be reworked to help deliver the “productivity improvements” that Hammond was demanding as part of the deal to lift the paycap. That will now come from staff losing one of their 27 days annual holiday entitlement.

Simon Stevens, the chief executive of NHS England, on Wednesday backed staff’s plea for a pay rise after seven years of wage restraint and said action was needed in order to help tackle the service’s growing problems in retaining staff. In a speech Stevens again made clear his view that the government should wholly fund whatever increase is finally decided, given the NHS’s deep financial problems.

Nigel Edwards, chief executive of the Nuffield Trust thinktank, said: “If the government makes a proposal like that obtained by the Guardian, staff, especially those paid least, will welcome the respite from a real-term squeeze on their wages which has cost them billions. With very serious shortages of staff, government is right to conclude that an austerity approach to the NHS workforce has reached its limits.”

But, Edwards added, losing a day’s leave would in effect be a pay cut of 0.4%, even with the salary increase.

Prof Anita Charlesworth, director of research at the Health Foundation, said: “The NHS needs urgent action to turn around nurse recruitment and retention. One in 10 nursing posts are unfilled and an increasing number of staff are leaving the NHS.

“Improving pay, especially for those on lower incomes, is very important. However, pay is not a panacea. Nurses report that two of the most important factors causing them to leave the NHS are worries about quality of care and lack of work-life balance. Any proposals on pay will need to be part of a wider programme to support nurses.”