The next Prime Minister must be a backer of Brexit, former Tory leader Iain Duncan Smith has said, as a number of leading Conservatives geared up to be the ‘Stop Boris’ candidate in the leadership election triggered by David Cameron’s bombshell resignation.

As the Tory party wrestled with the implications of the Brexit vote, Boris Johnson and Michael Gove continued to maintain a low profile, amid calls for them to take responsibility and spearhead Britain’s exit negotiations with the EU.

However, one senior Conservative MP and Johnson ally reportedly admitted to Sky News that for Vote Leave “there is no plan” for managing the aftermath of Brexit, in the expectation that Downing Street would have made a contingency plan.

Theresa May, Stephen Crabb, Nicky Morgan and Jeremy Hunt were all reported to be considering leadership challenges. Mr Johnson, who is expected to announce his candidacy later this week, is seen as the favourite, but could face a further challenge from fellow Leave supporters.

Ex-Defence Secretary Liam Fox, an ardent Brexit campaigner, became the first to publicly say he was considering a leadership bid and there is also speculation that Mr Gove could challenge for the top job.

But there were also calls for the Conservatives not to have a leadership contest at all. International Development Secretary Justine Greening said that Boris Johnson and Theresa May were the obvious frontrunners and should unite in the national interest, with a joint leadership “under one or the other”.

But in an apparent warning to pro-Remain colleagues thinking of running for the leadership, Mr Duncan Smith, the former Work and Pensions Secretary, said that after voting for Brexit, the public would be unlikely to accept a new Prime Minister who had wanted Britain to stay in the EU.

Home Secretary Theresa May backed Remain but kept a low profile during the campaign. Meanwhile, George Osborne, who until Thursday was considered a leading contender for the Tory leadership, may still run, but would face an uphill struggle to convince MPs and party members, because of his central role in arguing against Brexit.

"Whoever takes up that job... it would be very, very difficult for the public who have voted for leaving the European Union to find that they then had a prime minister who actually was opposed to leaving the European Union,” Mr Duncan Smith told BBC1's Andrew Marr Show.

"There was a clear decision, and what has to happen is delivery on that, and somebody who has been involved in that clearly has to be the case, because the Government itself had a view... which was to Remain, so now we need to change that position and actually deliver on this very clear mandate form the British people."

His comments were at odds with Ms Greening’s call for a May-Johnson unity leadership. In an article for ConservativeHome she said: “A leadership contest now is not in the interests of our country. It will mean our party focuses inward – at the very time our country most needs us to focus outward.

“Instead of a leadership contest which could take weeks and months, Boris and Theresa should agree to forge a deal which means they are a united leadership, under one or the other: a united leadership that for the sake of unity I hope the rest of our party could support.”

6 ways Britain leaving the EU will affect you Show all 6 1 /6 6 ways Britain leaving the EU will affect you 6 ways Britain leaving the EU will affect you More expensive foreign holidays The first practical effect of a vote to Leave is that the pound will be worth less abroad, meaning foreign holidays will cost us more nito100 6 ways Britain leaving the EU will affect you No immediate change in immigration status The Prime Minister will have to address other immediate concerns. He is likely to reassure nationals of other EU countries living in the UK that their status is unchanged. That is what the Leave campaign has said, so, even after the Brexit negotiations are complete, those who are already in the UK would be allowed to stay Getty 6 ways Britain leaving the EU will affect you Higher inflation A lower pound means that imports would become more expensive. This is likely to mean the return of inflation – a phenomenon with which many of us are unfamiliar because prices have been stable for so long, rising at no more than about 2 per cent a year. The effect may probably not be particularly noticeable in the first few months. At first price rises would be confined to imported goods – food and clothes being the most obvious – but inflation has a tendency to spread and to gain its own momentum AFP/Getty Images 6 ways Britain leaving the EU will affect you Interest rates might rise The trouble with inflation is that the Bank of England has a legal obligation to keep it as close to 2 per cent a year as possible. If a fall in the pound threatens to push prices up faster than this, the Bank will raise interest rates. This acts against inflation in three ways. First, it makes the pound more attractive, because deposits in pounds will earn higher interest. Second, it reduces demand by putting up the cost of borrowing, and especially by taking larger mortgage payments out of the economy. Third, it makes it more expensive for businesses to borrow to expand output Getty 6 ways Britain leaving the EU will affect you Did somebody say recession? Mr Carney, the Treasury and a range of international economists have warned about this. Many Leave voters appear not to have believed them, or to think that they are exaggerating small, long-term effects. But there is no doubt that the Leave vote is a negative shock to the economy. This is because it changes expectations about the economy’s future performance. Even though Britain is not actually be leaving the EU for at least two years, companies and investors will start to move money out of Britain, or to scale back plans for expansion, because they are less confident about what would happen after 2018 AFP/Getty Images 6 ways Britain leaving the EU will affect you And we wouldn’t even get our money back All this will be happening while the Prime Minister, whoever he or she is, is negotiating the terms of our future access to the EU single market. In the meantime, our trade with the EU would be unaffected, except that companies elsewhere in the EU may be less interested in buying from us or selling to us, expecting tariff barriers to go up in two years’ time. Whoever the Chancellor is, he or she may feel the need to bring in a new Budget Getty Images

Despite their victory Mr Johnson and Mr Gove have made no public statements since their initial response to the referendum result on Friday.

With the government under pressure from European leaders to trigger Article 50 immediately – placing the UK formally into the two-year process of withdrawing from the EU – the leaders of the Brexit campaign faced calls to take responsibility and lead Britain’s negotiations with Brussels.

Former deputy prime minister Lord Heseltine, who lamented the Brexit vote, saying the country had been “sold a fool’s promise”, said that Mr Johnson, Mr Gove and UKIP leader Nigel Farage must be in charge of negotiations, so that they would have no-one else to blame in the event of an adverse economic outcome for Britain.

"It is essential that the negotiations are conducted by Boris Johnson, Michael Gove and Nigel Farage, the architects of this policy,” he said. "Any other negotiating team will produce claims that those three would have achieved a better result and during the negotiations they will excuse any deterioration in Britain's position as a failure of the negotiators.

"They must be in charge and seen to be in charge.”

He warned that the situation for industry and commerce was "deteriorating day by day" with investment decisions being postponed because of uncertainty about what kind of settlement Britain will get from the EU.

The foreign ministers of the six founding EU member states have said Britain must activate Article 50 urgently to avoid prolonged uncertainty and instability, and to allow the EU to move on with a process of reform. Meanwhile, US Secretary of State John Kerry will come to London for talks with Foreign Secretary Philip Hammond, and will also visit Brussels. Mr Kerry has urged both sides to handle the negotiations responsibly to minimise the impact on the markets.