Nick Clegg will infuriate David Cameron's restive backbenchers on Wednesday by insisting he will not allow the coalition to be broken up early and telling them it is time to get back to governing from the centre, and end the game-playing at Westminster.

His reading of the riot act to the Tory right is likely to be seen as the kind of slap-down to Cameron's rebels that the prime minister himself feels too weak to administer because of the advance of Ukip.

The deputy prime minister will accuse Tory MPs of "disappearing into a parliamentary rabbit warren, obsessing over this new tactic or that new trick: paving legislation, enabling referendums, wrecking amendments".

After two weeks of Conservative battles over a European referendum and gay marriage, Clegg will also admit that the past fortnight has seen the coalition lacking leadership, focus and an ability to govern.

On Tuesday night 133 Conservative MPs, among them the environment secretary Owen Paterson and the Welsh secretary David Jones, voted on a free vote against the coalition's legislation to legalise gay marriage.

Clegg's speech was shown to Conservative leaders on Tuesday night in advance, but in reality there was little Cameron could do to stop Clegg portraying his party as the adult, if junior, partner in the coalition relationship. He will insist the behaviour of the Tory right will have left the public bewildered, but will argue that he will not allow the coalition to be distracted from its main task of fixing the economy.

Clegg's decision to lecture the Tory backbenchers and guarantee that the coalition will last until the general election in 2015 will infuriate the Tory rightwingers trying to engineer a break-up.

At the weekend Cameron speculated for the first time about the possibility of an early coalition break-up, but stressed this was not the aim, or his expectation. There have also been claims that No 10 is preparing contingency plans for an early break-up.

But at a hastily convened London press conference Clegg will defend the radicalism of the coalition, adding: "It still has work to do, and the best way for us to serve and improve Britain is by finishing what we started. To those voices who say that it will be in either, or both, parties' interests to prematurely pull the plug: I couldn't disagree more.

"In 2010 the British people dealt us this hand. And they will not forgive either party if we call time ahead of the election that has been legislated for in 2015 – destabilising the nation in the vague hope of short-term political gain."

He will also express his exasperation that at the point at which the country is facing the "most profound economic challenge in living memory", parliament is being clogged up by issues such as Europe and gay rights "simply because they cause the biggest political punch-ups".

The public will think MPs have taken leave of their senses, he will say.

Clegg's remarks may also frustrate to a lesser extent those Liberal Democrats warning that the party risks losing its identity if it does not do something dramatic to distance itself from a rightward-leaning Conservative party.

Clegg will contend there is no logic to ducking out early before the election, adding: "It is a nonsense to think such a move could suddenly win back those people who have never liked us going into government with the Conservatives."

But Clegg will hint that the Lib Dems may be suffering collateral damage due to Tory in-fighting distracting from the coalition's reform agenda. He will say: "Sincere policy debates and ideological differences are, and will continue to be, a part of coalition. But the parliamentary game-playing we've seen over the last few weeks discredits the importance of these issues, and it's an unwelcome distraction."

The two parties remain "two staunch opponents, working together to find answers to the most critical questions facing Britain today, pioneering major reforms that will stand the test of time".

But faced by a Conservative party that seems to feel forced to head to the right in the face of the threat posed by Ukip, he will insist that, so long as he remains deputy prime minister, the government as a whole will not vacate the centre ground. Claiming Ed Miliband sees a new centre ground taking shape on the left, he will say: "Some Conservatives insist the centre of gravity has swung the other way. They seize on people's reasonable concerns over things like immigration and welfare as proof the nation has shifted to the right. Yet in reality millions of people across Britain continue to shun the extremes of left."He will admit that as the election nears there will be further tensions between the parties, and both leaders will be under increasing pressure to act in their parties' interests as opposed to the national interest.

Clegg feels that the Conservatives have never reconciled themselves properly to the concept of coalition, partly because they were so sure they were going to win outright, and partly because the coalition deal was never put to any democratic forum of the Conservative party.

He will remind Tory MPs: "Whether you are the larger or smaller party, the fact is governing together in the public interest carries a cost. Making compromises; doing things you find uncomfortable; challenging some of your traditional support – these are the dilemmas the Conservatives are coming to terms with, just as my party has had to."