David Cameron has delivered a stark warning to the British people that a vote to leave the EU will be final and irreversible, as he stamps on suggestions that a better deal could then be negotiated and put to the electorate in a second referendum.

The move by the prime minister reflects growing irritation inside No 10 at claims by leading members of the Vote Leave campaign, and by London mayor Boris Johnson, that a no vote could strengthen the UK’s hand and force the EU to give more ground in another renegotiation, followed by a second vote.

A senior aide to the prime minister put out a statement saying it was simply “not credible” to suggest that a majority of the electorate could vote to leave the EU, only for the government and the EU to re-enter discussions to try to find a way to keep the UK in.

Speaking with the full authority of the prime minister, the aide said: “Some of those advocating ‘leave’ are suggesting that the referendum is just the first half and that if the majority of the UK public voted to leave, then the UK government would have a stronger hand to embark on a second negotiation with the rest of the EU and hold a second referendum. The prime minister is clear that is simply not going to happen. From the outset, he has been clear this will be a straightforward in/out choice. Leave means leave.”

He implied that those suggesting such an approach were trying to mislead people into thinking a no vote was not a risk, and accused them of lacking conviction about the merits of their own case.

“Trying to muddy the waters as they are, and suggest that we can have a second chance if we vote to leave, suggests that the leave campaign lacks confidence in its own case and is worried about the risks. Otherwise, it would unambiguously advocate a clean exit.”

The other 27 EU nations, he added, “are not going to countenance a second renegotiation with a country that has already decided to leave. Instead, attention would turn to the process for leaving – a protracted negotiation under article 50 of the Lisbon treaty.”

Senior sources said Cameron wanted to force the Vote Leave campaign to come clean about the full implications of an EU exit, rather than pretend that a no vote would not necessarily mean no.

Cameron has made it clear that he would prefer the UK to stay in the EU if, as he hopes, he secures a good deal from the EU on the UK’s terms of membership. But he has not made clear whether he will definitely campaign to stay in if the negotiations fail to deliver much improvement on the status quo. Cameron has pledged an in/out referendum before the end of 2017. Ministers believe the most likely date is autumn next year.

Pro-EU figures in government, nervous that support for getting out of the EU may be on the rise, want to squash any suggestion that the UK could do as Denmark and Ireland did, when they asked the people a second time after no votes in referendums on treaty changes, securing eventual yes votes.

The Observer can reveal the findings of a major report into the effects on UK farming and the food industries of a British exit. The study by Agra Europe, a respected London-based firm which analyses agricultural policy, says that only the top 10% of UK farms – the “superefficient” – would be able to survive financially without EU subsidies from the Common Agricultural Policy (CAP). The report says: “In the period to 2013, EU subsidies to UK farmers amounted to around €3.2bn a year. In terms of the individual farmer these subsidies of around €200 per hectare generally represent around 35-50% of total gross income. For a majority of farms, they represent the difference between profit and loss.” It says the UK government, if outside the EU, would probably aim to cut total subsidies to farmers dramatically, leaving many in dire straits.

Cameron’s intervention shows how his attempt to avoid taking sides until the current renegotiations with the other 27 member states are complete is coming under strain, as senior business figures back continued membership. Last week, the governor of the Bank of England, Mark Carney, said being inside the EU had increased the openness and dynamism of the UK economy and that it had been one of the drivers of its strong economic performance in recent decades.

While Carney conceded there was a need to ensure the economy was safeguarded from potential instabilities to the UK caused by a more closely integrated euro, he said free movement of labour helped plug skills shortages and fostered economic growth.

Johnson, a leading contender to succeed Cameron when he steps down in 2020, has made known that he is interested in the “double referendum” and has hinted he might back a no vote first time round, on the assumption it would not be final but would shake the EU to its senses and persuade other members eventually to give the UK what it wants.

Dominic Cummings, a former special adviser to Michael Gove, who is now director of Vote Leave, wrote on his blog in June: “If you vote yes, you won’t get another vote for another 40 years – if ever. You should vote no to Cameron’s rubbish deal. If you vote no, you will force a new government to negotiate a new deal and give you a new vote. A no vote is much safer than a yes vote.”