David Cameron is to move fast to capitalise on his general election victory by introducing key elements in the Tory manifesto for an EU referendum and the scrapping of the Human Rights Act that will be overseen by Michael Gove.

As Labour is distracted by contests for the leadership and deputy leadership of the party, the prime minister will outline plans for a raft of legislation in the Queen’s speech on 27 May that will transform the nature of British politics.

The prime minister, who has a modest majority, will move to entrench the Tories’ position by pressing ahead with radical boundary changes to overcome what is seen as a bias in favour of Labour. But Downing Street is to scrap plans to cut the number of MPs from 650 to 600, according to the Sunday Times.

The Tory leadership steered clear of the airwaves over the weekend as Downing Street allowed the media to focus on the soul-searching under way in the Labour party after its worst defeat since 1987.

But the prime minister indicated the direction he intends to take after securing the first overall Tory majority in 23 years when he promoted George Osborne to the additional post of first secretary of state, making him the most senior figure in the EU negotiations after Cameron himself. The Queen’s speech will include legislation for a referendum on the EU.

Gove, who lost his job as education secretary last year after the Tory campaign director, Lynton Crosby, warned that he had become overly toxic, will take charge of the scrapping of the Human Rights Act as the new justice secretary. The appointment sets up a potential conflict with Theresa May, the home secretary, who was furious with Gove when he briefed against officials in her department about the government’s anti-extremism strategy.

David Mundell, the Tories’ only MP in Scotland who was a junior Scotland Office minister in the last parliament, is expected to be promoted to the cabinet as Scotland secretary. He will take charge of implementing the cross-party Smith commission which called for the Scottish parliament to be given full power to set income tax rates and bands and about £3bn of welfare powers including the housing elements of universal credit.

But Nicola Sturgeon, the SNP first minister whose party is the third largest contingent at Westminster with 56 MPs, made clear that the prime minister should go further. Sturgeon told the Andrew Marr Show on BBC1: “Our manifesto set out very clearly that we would want to move to full fiscal responsibility. You know clearly that will take a number of years to implement. What we’re arguing for and what we will argue for is priority devolution of powers over business taxes, employment, the minimum wage, welfare, because these are the levers we need to grow our economy faster, to get more people into work.”

The prime minister was also warned that he could face trouble on Europe as David Davis, the former Tory leadership contender, called on him to demand the right to exercise a UK opt-out from all EU legislation. This would amount to a complete rewriting of the rules of the single market which is not currently on the prime minister’s agenda.

Davis told the Andrew Marr Show on BBC1 that Britain should be given its own “Luxembourg compromise” – a mechanism available to all member states which says they can opt out in areas where there is no national veto if a vital national interest is at stake. The mechanism, which is rarely used, was devised after a row with Charles de Gaulle in the mid 1960s.

“The main [demand] is that in the future we are able to say to the Europeans look, this is too far for us, and opt out. Not a veto, an opt-out,” Davis said. “There is one already for France. There’s a thing called the Luxembourg compromise. France has on a couple of occasions said this is going to damage our shipping industry, we don’t want it, and they’ve effectively brought it to an end.”

But Lord Mandelson said that changing the rules of the single market, which are decided by “qualified majority voting” in which no member state has a veto, would work against British interests. The Davis proposal would allow less liberalising states, such as France, to impose protectionist measures.

Mandelson told the Andrew Marr Show: “If [David Cameron] goes in to those negotiations with an agenda supplied to him by his madcap back-benchers, then he’s going to get precisely nowhere. If he goes in with a slightly more intelligent reform agenda, which, by the way, there is a very large constituency of support for across the European Union, then I think he will get somewhere.”