Theresa May will threaten to take Britain out of the single market unless the UK is given full control of its borders in a significant Brexit speech designed to counter claims she has no plan for leaving the EU.

The Prime Minister will outline her “vision for Britain outside of the EU” in a major speech later this month that will focus on the economy and immigration.

Both David Davis, the Brexit Secretary, and Boris Johnson, the Foreign Secretary, are having “significant” input into the speech, sources said.

However, Liam Fox, the Trade Secretary considered one of the “three Brexiteers” alongside Mr Davis and Mr Johnson, is understood to have been sidelined.

The speech will be seen as a retort to claims of “muddled thinking” in Mrs May’s Government by Sir Ivan Rogers, who on Tuesday resigned as Britain’s EU ambassador after a series of rows with Downing Street.

Last night the Government announced that Sir Ivan’s successor will be Sir Tim Barrow, a close ally of Mrs May and Mr Johnson and former ambassador to Russia who has experience negotiating with Vladimir Putin.

He was described by ministers as an “optimist” whose outlook is in “stark contrast” to the “pessimism” from Sir Ivan, which infuriated Mrs May’s senior team.