Theresa May has risked a backlash after clearing out a number of white, male ministers and replacing them with up-and-coming women and MPs from ethnic minority backgrounds.

The Prime Minister used the second day of her reshuffle to make her frontbench “better reflect the country”, but faced accusations that some people were being unduly pushed out.

It came as an analysis by a think tank found the Cabinet now had a greater share of ministers who went to private schools than before the reshuffle.

Ms May’s changes on Tuesday followed the chaos of Monday, which saw some top ministers refusing to move from posts and a resignation.

She said: “This Government is about building a country fit for the future – one that truly works for everyone with a stronger economy and a fairer society.

“This reshuffle helps us do just that by bringing fresh talent into Government, boosting delivery in key policy areas like housing, health and social care, and ensuring the Government looks more like the country it serves.

“It also allows a new generation of gifted ministers to step up and make life better for people across the whole UK.”

Theresa May's cabinet reshuffle: Key positions

Among those joining the ministerial ranks for the first time are Richmond MP Rishi Sunak at the Ministry of Housing, Stratford-on-Avon MP Nadhim Zahawi at the Department for Education and South East Cambridgeshire's Lucy Frazer, who is joining the justice team.

Shailesh Vara returns to the Government after a spell on the backbenches as a junior minister at the Northern Ireland Office.

Another move saw Suella Fernandes – leader of the influential pro-Brexit European Research Group – to the department responsible for the UK's departure from the EU, something which increases its ministerial team by one.

Meanwhile, political casualties included Mark Garnier, who lost his job as trade minister just weeks after being cleared by an investigation into allegations of inappropriate behaviour towards a female member of staff, including asking her to buy a sex toy.

MP Suella Fernandes becomes a minister at Dexeu (ITV/REX)

With other departures including the likes of Robert Goodwill, Philip Dunne and John Hayes, one male backbencher raised concerns.

Philip Davies MP said: “It certainly does not do anyone any favours to promote people who are not ready for promotion just because of their gender or race.”

But the Prime Minister's official spokesman said: "It is about getting the right Government in place to deliver for the British public.

"That also includes delivering a Government that better reflects the country which it serves."

Research from the Sutton Trust showed 34 per cent of the 29 ministers attending cabinet went to independent schools, compared with 30 per cent of her first cabinet last year.

The figures are still lower than under David Cameron, who appointed a cabinet in 2010 in which 62 per cent of its members were privately educated, and 50 per cent in 2015.