David Cameron has sacked the Tory party chairman Grant Shapps from the cabinet after a series of embarrassing revelations about his alleged attempts to mould his image on social media.

In a humiliating blow after he helped to deliver the first Tory parliamentary majority in 23 years, Shapps was demoted to the lesser role of minister of state at the Department for International Development.

Shapps had attended the cabinet as Tory co-chairman and as minister without portfolio at the Cabinet Office. His humiliation was compounded by the prime minister’s decision to promote his fellow Tory co-chairman Lord Feldman to the post of full chairman of the party with a seat in the political cabinet.

The move by Cameron came as he prepared to tell a meeting of the first Tory-only cabinet in 18 years that he leads Britain’s “real party for working people” which will make job creation and the expansion of childcare its main priorities. In a bold attempt to claim traditional Labour territory, the prime minister will declare that every step taken by his government will be designed to help people striving for the dignity of a job.

Cameron, who was given a rapturous reception when he addressed the first post-election meeting of the 1922 committee of backbench Tory MPs, will address the cabinet after appointing a series of ministers from modest backgrounds to what was quickly called the Tories’ first blue-collar cabinet.

Sajid Javid, the son of a Pakistani-born bus driver who arrived in Britain in 1961 with £5 in his pocket, was promoted from culture secretary to business secretary.

David Cameron unveils first Tory-only cabinet in 18 years Read more

Priti Patel, the daughter of Ugandan Asian immigrants, is promoted from a junior post at the Treasury to become one of a series of women with seats round the cabinet table. Patel will attend cabinet as employment minister as the prime minister seeks to deliver on his commitment that women will make up a third of his top ministerial team.

Other female newcomers to the cabinet table include Amber Rudd, as energy and climate change secretary, and Anna Soubry as minister for small business. Penny Mordaunt becomes the first woman to serve as armed forces minister while Anne Milton becomes the first female Tory government deputy chief whip.

Boris Johnson will attend meetings of the political cabinet, suggesting that he will take a full government post when his term as London mayor ends next year. The BBC was given warning that it faces a tough fight in the negotiations over the renewal of the licence fee and its royal charter when the Thatcherite veteran MP John Whittingdale replaced Sajid as culture secretary.

Whittingdale, the chairman of the Commons culture select committee since 2005, has described the £145.50 licence fee as “worse than the poll tax” and unsustainable in the long term.

The appointment of Whittingdale, who served as Margaret Thatcher’s political secretary in her final years in No 10, and of Patel suggests that Cameron is keen to bind the Thatcherite right into his EU referendum plan. Patel worked for the late Sir James Goldsmith when his Referendum party fielded candidates in the 1997 general election.

Cameron’s arrival at the 1922 committee meeting in Westminster was met with cheering by MPs. They banged their desks to welcome his success in securing the first Conservative parliamentary majority since the 1992 election. “We will have a ministry of all the talents,” the prime minister said of his new cabinet.

Cameron was in relaxed mood after his surprise win as he held a copy of the Tory manifesto at the meeting, telling the newly elected MPs that he had three priorities. First, he said, he wanted the Conservatives to be seen as the real party of working people, a point he illustrated by appointing the campaigning MP for Harlow, Robert Halfon, as the new deputy chairman.

The prime minister said the Tories needed to show they were the party of compassion by pressing ahead with reforms to welfare and education. Finally, he said, the Tories needed to bring the UK together.

Cameron will tell the cabinet on Tuesday of the Tories’ new approach: “I want everyone around this table to remember who we’re for. Every decision we take, every policy we pursue, every programme we initiate, never forget: we’re here to give everyone in our country the chance to make the most of their life.

“The pundits might call it ‘blue-collar Conservatism’, others being on the side of hardworking taxpayers. I call it being the real party for working people: giving everyone in our country the chance to get on, with the dignity of a job, the pride of a paycheck, a home of their own and the security and peace of mind that comes from being able to support a family.”

“And just as important – for those that can’t work, the support they need at every stage of their lives.”

The prime minister will highlight his approach by announcing that the Queen’s speech on 27 May will include a bill to deliver 3 million new apprenticeships and full employment. It will also include a bill to deliver on the Tory manifesto commitment to double the amount of free childcare for working parents with three- and four-year-olds receiving 30 hours a week.