Announcing her candidature for Conservative Party leader and Prime Minister, Theresa May declared “Brexit means Brexit.”

Brexit, then, was always likely to influence the appointment of more Brexit-minded MPs to government positions under her premiership.

With “impressive ruthlessness” the backbones of David Cameron’s cabinet – George Osborne, Michael Gove, Nicky Morgan and others – have been dismantled. We have witnessed not a reshuffle of ministers but wholesale change in the make-up and, May will hope, the branding of the government.

In 2002, May famously warned the Conservative Party to shed its image as being Britain’s “nasty party”. In her maiden speech as Prime Minister on Wednesday she pledged this government would not to be driven by “the privileged few”.

Going by this speech, the mission of the new administration will be to advance social justice, exit the European Union and unify a divided United Kingdom as “one nation”. By her cabinet shake-up she clearly seeks to unite a fractured Tory party too.

Key appointments like Philip Hammond (Remainer) as Chancellor, and of Eurosceptics like David Davis as Secretary for Exiting the EU, Liam Fox as Secretary for International Trade show a willingness to unify. So too does the appointment of May’s recent Tory leadership rival (and Leaver) Andrea Leadsom as Environment Secretary.

The appointment of Boris Johnson as Foreign Secretary has raised eyebrows, but as leader of the Leave campaign – a vote he arguably swung and won – surely the onus should be on him to spearhead Britain’s new era of international relations.

In the referendum’s aftermath, Remainers complained prominent Leavers Johnson, Gove and UKIP’s Nigel Farage were allowed to abdicate responsibility. With BoJo’s appointment the Brexiteer-in-chief will not be afforded opportunity to fade into the shadows.

May’s way looks set to be calm and considered, with the EU exit gradual. From a Northern Ireland perspective, the appointment of James Brokenshire as Secretary of State – a former lawyer, security and immigration minister at the Home Office – may fit another piece of the May jigsaw.

This week Britain has a new Prime Minister and new government. Both put the onus on Brexiteers to negotiate the best deal possible for the UK leaving the EU, and on both sides of the Conservative Party to come together.

To May, the Brexit vote means Brexit and bringing more Brexiteers on board too.