Theresa May has insisted in her first major interview since taking office that there will be no snap general election before 2020. The prime minister told The Andrew Marr Show the country needed a period of stability after the shockwaves of the pro-Brexit vote, and that the UK should be prepared for “difficult times” ahead, despite better-than-expected economic indicators.

Pressed on whether she was tempted to call a snap election, with polls showing she could increase her majority of just 17 to 130 seats, May said: “I’m not going to be calling a snap election. I’ve been very clear that I think we need that period of time, that stability, to be able to deal with the issues that the country is facing and have that election in 2020.”

Under the Fixed-Term Parliaments Act 2011, there is a statutory five-year gap between elections, unless two-thirds of the Commons agree, or there is a motion of no confidence in the government. Any other circumstances would require a change in the law.

Discussing her plans for securing the best Brexit deal possible for the UK, the prime minister insisted controls on the movement of people from the EU to Britain needed to be imposed as part of a deal with Brussels. Brexit secretary David Davis will make a statement to the Commons this week on the government’s emerging position on the terms of withdrawal and what kind of relationship the UK wants with the EU, May said.

Her decision not to call an early election eases the immediate pressure on Labour, but leadership contender Owen Smith has warned that his party faces a “decade of doom” under successive Tory governments if Jeremy Corbyn is re-elected leader. Smith supporters claim that the leadership contest could still be far closer than polls have suggested.

Owen Smith addresses a campaign rally in Hammersmith, London, last month. Photograph: Tolga Akmen/LNP/Rex/Shutterstock

Writing in the Observer before a major speech on Sunday, Smith says that, under Corbyn, the party has never been further from power and will be staring at “electoral oblivion” if Corbyn is chosen for a second time on 24 September.

Corbyn’s supporters are confident that the Labour leader is heading for a thumping win and another huge mandate in the contest, and say that polling suggests he is trouncing Smith among the more than 600,000 members who are eligible to vote.

But the anti-Corbyn Saving Labour campaign, which says it has conducted detailed investigations into polling statistics and voting intentions, claims that the reality is that the contest is on a “knife edge”.

Former Labour MP Reg Race, who is working for Saving Labour, says he is deeply sceptical of polling figures suggesting that trade union affiliates will vote for Corbyn by 62% to 38%, while those who have paid £25 to become registered supporters will do so by 74% to 26%. He says Saving Labour recruited 120,000 new anti-Corbyn members who have not been picked up by pollsters. “The reality is that this is too close to call,” Race said.

Smith’s camp also claim their man can still win if they can convince enough people that Labour has no hope of winning under Corbyn. In his article, the former shadow minister for work and pensions paints Corbyn as irresponsible for surrounding himself only with “people who agree with him” and for “defining himself against his own party instead of the Tories”.

“Knowingly marching off to electoral irrelevance is a gross betrayal of the people all Labour members and supporters – new and longstanding – came into politics to help,” he writes. “If we give up on winning the next election, or falsely claim to be on course to win, we are willing accomplices for every Tory cut.”

on Monday, the Labour leadership will try to rally the disunited parliamentary party behind opposition to Conservative plans to cut corporation tax and capital gains tax when MPs return to the Commons from the summer break to debate the finance bill.

Labour’s opposition to the tax cuts will be led by the shadow chief secretary to the Treasury, Rebecca Long-Bailey, who said that the debate was an opportunity for the party to stand four-square behind the leader.

Long-Bailey said: “The government wants to reduce corporation tax to 17% by 2020. If we thought these cuts would benefit business and would increase investment, we would be fully behind them. But there is no evidence for that.”

She said Labour’s emphasis was not on tax cutting but investment, adding that she was confident that if Corbyn won, the party would quickly reunite.

“It is just a matter of time before everyone falls into line. There will be a lot of discussions between disgruntled MPs. There need to be discussions and negotiations, and I think they will take place.”

Privately, however, critics of Corbyn say that if they do not succeed in removing him in the current contest, they will attempt to trigger another contest some time next year.