Theresa May will carry out her long-awaited cabinet reshuffle on Monday, after admitting she will only remain at No 10 “as long as people want me to serve”.

The Prime Minister appeared to acknowledge her fate is in the hands of Conservative MPs – while again insisting she intended to lead her party into the next general election, not due until 2022.

“I’m not a quitter. I’m in this for the long term,” she told the BBC’s Andrew Marr Show, in an appearance to kickstart the new political year.

But, pressed on whether she could survive to fight another election, she replied: “Obviously, I serve as long as people want me to serve,” – the phrase she used when under threat from Tory backbenchers last year.

Ms May will attempt to assert her authority with her first major cabinet reshuffle since the immediate aftermath of last year’s election debacle, which The Independent has been told will happen on Monday.

However, despite pressure last year to sack both either Chancellor Philip Hammond or Boris Johnson, the Foreign Secretary – or both – all the most senior ministers are now expected to remain in their posts.

A mooted plan to shift Mr Johnson into a beefed-up business department, with responsibility for Brexit planning, appears to have been dropped after he made clear he would not agree to it. If Mr Johnson has indeed successfully fought off the Prime Minister’s attempt to demote him, it will be seized upon as evidence of her continued weakness.

Justine Greening, the Education Secretary, is expected to be the most prominent casualty in the shakeup, amid her apparent unease about much of education policy. A grammar schools sceptic, Ms Greening is seen as too close to the teaching unions and lacking enthusiasm for expanding the free schools programme.

Most controversy centres on whether there will be a promotion for Health Secretary Jeremy Hunt, or even for Chris Grayling, the under-fire Transport Secretary.

Ms May needs to replace Damian Green, who was sacked as Cabinet Office minister for lying over the pornography found on his office computer, who chaired multiple, crucial Brexit committees.

Patients’ groups and health unions are likely to greet moving Mr Hunt into that role – even without the First Secretary of State title enjoyed by Mr Green – with fury, amid the growing winter crisis in the NHS.

Jon Ashworth, Labour’s Shadow Health Secretary, said: “If she promotes this Health Secretary tomorrow, it’s a betrayal of those 75,000 people in the back of ambulances.”

Similarly, Mr Grayling is under fierce pressure over allegations that he has disguised a likely £2bn taxpayer bailout for the private firms which run the East Coast rail line.

As well as Mr Hammond and Mr Johnson, the other two most senior ministers – Amber Rudd, the Home Secretary, and David Davis, the Brexit Secretary – are also expected to remain in place.

Party chairman Patrick McLoughlin, Business Secretary Greg Clark and Andrea Leadsom, the Leader of the Commons, are also tipped for the chop, or to be moved.