Voters are facing a stark choice between a Tory no-deal Brexit at the end of next year if the Conservatives win a majority at the general election and a second referendum with the option to Remain if they fail to do so, the former Tory cabinet minister David Gauke has said.

Gauke, who resigned from the Conservative party last week and will fight the South West Hertfordshire seat he has represented since 2005 as an independent, told the Observer it would be “impossible” for a Tory government to conclude a complex agreement with the EU within such a short time, meaning no-deal would be inevitable, as Boris Johnson would refuse to extend the transition period.

The former justice secretary said he decided to leave the party because it had become “obsessed with leaving the EU at any cost while failing to take into account the many challenges and potential downsides”.

He has come round to the idea of a second referendum, believing the British people should have the right to say whether they really want to crash out of the EU on terms far more damaging to the country and the economy than those suggested by Leavers during the 2016 referendum.

Gauke, who is also a former Treasury minister, said it would take until March next year for the EU even to agree a mandate or remit for trade talks with the UK, meaning negotiations could not start in earnest until then. Under the withdrawal agreement, the end date of the transition period has been set as 31 December 2020.

However, there would also need to be around three months after a deal had been struck to allow EU member states to ratify an agreement, leaving only about six months to complete the hugely complex talks which trade negotiators estimate will take at least three years. “There is next to nothing that you can get done in six months,” Gauke said.

The withdrawal agreement also states that the transition or implementation period could be extended by one or two years, so long as an extension was agreed by 1 July next year. But Johnson has made clear he would not apply for an extension in any circumstances.

The result, Gauke said, was that there would be “no way out” for a majority Conservative government under Johnson that would avoid the disaster of a no-deal outcome.

“I don’t see what the escape route is if there is a Conservative majority. Will we withdraw [leave the EU] at the end of January 2020? Yes. Will the prime minister seek an extension to the implementation period before July 1 next year? No. Will a comprehensive free trade agreement be completed and ratified before December 31 2020? No.”

If the Tories were deprived of a majority, he believed there would be a majority in parliament to resolve the Brexit issue through a second referendum. Labour has said it would put any Brexit deal it negotiated back to the people with the option to Remain.

The country is polarised between those who would pursue a hard Brexit, which is where the prime minister is, and Remain David Gauke

Gauke said he would be putting the stark choice to voters on the doorstep, having “reluctantly” come round to the view that another referendum was now the best and only way to avoid a no-deal.

“My position was that if the country could unite around a soft Brexit that would be the least worst way through. But it is now very clear that the country is not going to unite around a soft Brexit. There is nobody really advocating a soft Brexit. The country is polarised between those who would pursue a hard Brexit, which is where the prime minister is , and Remain.

“And if those are those the two choices – and I think they are – then I would favour Remain. Those are the choices that should be put back to the British people.”

Politically, it would be impossible for Johnson to extend the transition, he said. “I think he does not have the political space to seek an extension,” Gauke added. “The parliamentary party would not allow him to do so, the membership would not allow it and his cabinet would I suspect not permit it. I think he would live in fear of a senior cabinet minister becoming the darling of the parliamentary party and membership [by resigning] and trying to inherit the crown.”

In South West Hertfordshire, Gauke’s majority over Labour at the 2017 election was just under 20,000 meaning he will have an uphill struggle, particularly as the pro-Remain Liberal Democrats will be fighting the seat.