David Cameron will this week attempt to reclaim the political initiative as MPs return to Westminster after a bruising summer marked by an outbreak of internal dissent over his leadership.

The Prime Minister will seek to reassert his authority over his restive Conservative Party with his first Cabinet reshuffle since the coalition took office in 2010.

At the same time ministers are preparing a series of high-profile announcements intended to inject new life into the moribund economy and pull the country out of recession.

Mr Cameron used an article for a Sunday newspaper to declare his determination to end the "paralysis" and "cut through the dither" that was holding the country back. His comments were seen as a riposte to Tories such as London Mayor Boris Johnson, who accused him of "pussyfooting around", and Tim Yeo, who questioned whether he was "man or mouse".

However, he faces an immediate challenge from the Tory right, with David Davis - who fought him for the party leadership in 2005 - setting out his alternative strategy for growth. Before proceedings in the Commons have even started, Mr Davis will use a lunchtime speech to the Centre for Policy Studies think-tank to call for a radical programme of cuts to taxes, regulation and public spending to kick-start the economy.

Meanwhile, Mr Cameron's party management skills will be put to the test as he seeks to re-boot his Government with a reshuffle of his top team. Many of the most senior figures are expected to remain in their present posts - including Chancellor George Osborne, Foreign Secretary William Hague, Home Secretary Theresa May, Education Secretary Michael Gove, Work and Pensions Secretary Iain Duncan Smith and Defence Secretary Philip Hammond - leaving limited room for manoeuvre.

Much attention has focused on the key role of Conservative Party chairman. Baroness Warsi has publicly appealed to Mr Cameron to allow her to carry on in the post, but some Tory MPs want to see her replaced with a big hitter who can galvanise support for the party. Employment minister Chris Grayling and housing minister Grant Shapps have been touted as possible alternatives from outside the Cabinet.

Mr Cameron may carry out a more far-reaching shuffle when he comes to the middle and lower ministerial ranks, taking the opportunity to get rid of under-performers and to blood new talent from the 2010 intake of new MPs.

Mr Cameron's official spokesman refused to comment on the timing or content of the expected reshuffle. But he confirmed that the regular weekly meeting of Cabinet will take place on Tuesday morning at the usual time. This sparked some speculation among Westminster observers that any Cabinet-level changes could take place later today to allow the new team to be in place in time for Tuesday's meeting.

Downing Street also released a schedule of ministerial engagements over the coming week, which includes events for some of those who have been tipped for the chop, including Justice Secretary Kenneth Clarke.