DAVID Cameron and Nick Clegg will today relaunch their bruised and battered Coalition Government, recommitting themselves to the primary task of saving Britain's ailing economy and "whatever needs done to succeed".

After weeks of sustained criticism and bad headlines culminated in a drubbing for both the Conservatives and the Liberal Democrats in the local elections, the Prime Minister and his deputy will try to convince the public they understand the hardships people are enduring.

However, the pair will make clear that – despite the latest rejection of austerity measures in elections in France and Greece – the Coalition's determined drive to reduce the deficit will continue.

"In these perilous times, it's more important than ever for Britain we stick to it," Mr Cameron will say. "I don't hide from the scale of that challenge or from the message sent by voters in many places in last week's elections. I'm listening. I'm leading. I get it. There are no closed minds, no closed doors in Downing Street," he will insist.

It comes two years on from their famous "wedding party" in the Downing Street rose garden, marked by light-hearted exchanges between the two men at a press conference after winning power.

In contrast, the Coalition's relaunch this afternoon at a factory in Essex will see a marked mood change to one of solemn determination. The renewal of their "marriage vows" marks the start of another crucial week for the Government with the announcement tomorrow in the Queen's Speech of its legislative programme for the new parliamentary session.

This is set to include laws on drug-driving; on enterprise to cut red tape, control excessive boardroom pay and strengthen competition; on allowing mothers and fathers to share parental leave; on splitting retail and banking operations; and on increasing internet surveillance.

The Queen's Speech will be followed on Thursday by the appearance at the Leveson Inquiry of Andy Coulson, the former No 10 communications chief and ex-News of the World editor. On Friday, it will be the turn of Rebekah Brooks, the former News International chief executive, to give evidence.

Mr Coulson and Ms Brooks threaten to throw more unwelcome light on the Tories' – and in particular Mr Cameron's – relations with Rupert Murdoch and his former executives.

After Tory backbencher Nadine Dorries recently branded the Prime Minister and his Chancellor, George Osborne, two out-of-touch "posh boys", the unease on Conservative benches about the Government's direction has grown.

Some Tory MPs have set out their agenda for an "alternative Queen's Speech", including traditionalist right-wing demands for a referendum on repatriating powers from Brussels and an expansion of grammar schools in England. They have rejected what they regard as LibDem obsessions – gay marriage and Lords reform.

Tory backbencher Nick Boles insisted things needed to improve "soon and over the next few months but then sustained throughout the next two or three years". He said: "By 2014 people will be saying to themselves, 'Is my life better? Is it heading in the right direction? Has the country got out of the hole the last government left them in?' And if they think the answer to that is yes, I'm confident we can do well at the next election."

After Mr Clegg cocked a snook at Tory traditionalists by insisting he would press harder for constitutional reform in the face of their opposition, more LibDem recriminations spilled over yesterday.

Simon Hughes, the party's deputy leader, again pointed out the Conservatives did not win a majority at the General Election. "It may be uncomfortable for the Tories – some of whom think they are born to rule – but unfortunately the electorate didn't agree with them," he said.

However, senior Tory backbencher John Redwood said it would be "silly" to go ahead with major constitutional reform when there was no consensus on what form it should take.

Today in Essex, Mr Cameron will set out what he will describe as the "unvarnished truth", that the damage done by the economic crisis has been greater than anyone had thought and the first-quarter growth figures – which showed Britain back in recession – had revealed a tough task getting even tougher.

The ambition, he will explain, is not only to cut the national deficit but also to build a recovery not on debt but on growth.

In his remarks, Mr Clegg will dismiss claims the Coalition has an "ideological obsession" with shrinking the size of the state, arguing there is a "clear moral responsibility" to deal with the deficit and not leave it to future generations. will sayy: "Ducking the tough choices would only prolong the pain, condemning the next generation to decades of higher interest rates, poorer public services and fewer jobs."