Labour's promise to "get Brexit sorted" within six months of winning power has been dismissed as "fairytale politics" by the Conservatives in the first clash of the election campaign on the issue.
In a speech in Essex, Jeremy Corbyn said his plan to get a better deal and then put it to the public in another referendum was "clear and simple".
He said a deadline to hold the vote next summer was "realistic and doable".
But the Tories said Labour's plan would result in "paralysing uncertainty".
However, the Conservative commitment to negotiate a new free trade deal with the EU in just over a year is also coming under scrutiny.
It took seven years for the EU to conclude a free trade deal with Canada, an agreement which many Brexiteers see as a template for the UK. Any deal would need to be agreed by all 27 remaining EU states before it could come into force.
Michael Gove, the minister in charge of Brexit planning, said a majority Conservative government would "absolutely not" extend the transition period after the UK's departure from the EU - under Mr Johnson's deal it is due to end at the start of 2021.
Pressed on whether this could ultimately lead to a no-deal exit - with the UK defaulting to World Trade Organisation rules - if no free trade deal could be agreed by that point, he pointed out that Mr Johnson had been able to secure major changes to the current withdrawal agreement in "just 90 days".
Ex-Justice Secretary David Gauke, who lost the Tory whip after rebelling over Brexit, said it would be "reckless" to exit transition without a trade deal and MPs must get a vote before this happened.
It was a clear promise. As @RobertBuckland said 'Parliament has a legitimate role to play'. I agree.— David Gauke (@DavidGauke) November 5, 2019
Looks like the Conservative message is "we'll be out on WTO terms by 2021". I have to say - that is reckless. https://t.co/CgcG5fVU3a
The political parties are ramping up their election campaigning, ahead of the official start to the five-week campaign period at just after midnight on Wednesday.
Brexit is set to be a crucial issue when voters go to the polls on 12 December, with Mr Johnson insisting the UK will leave in January if he wins power.
'Race to the bottom'
The UK and US have both said they are eager to do a free trade deal after Brexit, and in August, President Donald Trump predicted that leaving the EU would be like losing "an anchor round the ankle".
But in a speech in Harlow - a target seat for Labour - Mr Corbyn accused Mr Johnson of seeking to "hijack Brexit to sell out the NHS" to American firms in a future trade deal with the US.
The PM's strategy could see an extra £500m a week spent on buying medicines, he claimed, as well as leading to a "race to the bottom" on workers' rights and product standards.
Mr Johnson has insisted the NHS would "not be on the table" in post-Brexit trade talks with the US.
The BBC's Reality Check correspondent Chris Morris said the £500m figure was a theoretical worst-case scenario in which the prices of all medicines used in the NHS were the same as the prices of those medicines in the US.
However, he said in practice that was highly unlikely - although there was no question US pharmaceutical companies would lobby aggressively for greater access to the NHS, and the ability to set higher prices.
Mr Corbyn claimed Boris Johnson's EU exit deal will "unleash Thatcherism on steroids".
"Given the chance, they'll slash food standards to match those of the US where 'acceptable levels' of rat hairs in paprika and maggots in orange juice are allowed," he will claim.
"And they will put chlorinated chicken on the supermarket shelves."
'Clear and simple'
If elected next month, Mr Corbyn said he could strike a "sensible" new deal with the EU within months "based on terms we have already discussed with the EU - including membership of a customs union and absolute guarantees on workers rights.
At the same time, a Labour government would plan for a new public vote in June or July.
"Labour's plan would get Brexit sorted so a Labour government can get on with delivering the real change Britain needs," he told activists.
"Only a Labour government would put a decision in your hands... It cannot be left to the politicians...The Brexit crisis must be resolved but it must done democratically."
Mr Corbyn has refused to say whether he would back Leave or Remain, but said he would "immediately carry out" the public's decision so the country could "move on".
Speaking at the same event, shadow Brexit secretary Sir Keir Starmer said a Labour government would "rip up" Mr Johnson's deal with the EU, describing it as a "trap door" to a no-deal exit at the end of the transition period.
He said reaching a new economic and security relationship with the EU was a "massive task" and there would be "no safety net" if the talks were not concluded next year.
But Mr Johnson said another referendum would be a "disastrous, clamorous" waste of time.
Addressing ministers in Downing Street at his final cabinet meeting before Parliament is dissolved for the election, he said his government "could be proud" of what it had achieved on Brexit, despite failing to meet his "do-or-die" deadline to leave on 31 October.
"We've achieved something people thought we really couldn't do - get a great new deal on Brexit from EU - they said it couldn't be done.
"The choice before country is really very clear - do you want to go forward with our agenda which is to get Brexit done and then get on with delivering all the wonderful things we want to do for this country... or do you want to waste 2020?"
And Mr Gove suggested Mr Corbyn was incapable of negotiating a new Brexit deal in the way Mr Johnson had done.
"It is a fairy tale if you imagine Jeremy Corbyn can get Brexit done. His policy on Brexit has been constructed by a terminally weak leader in order to paper over the cracks in his party."
And on a visit to a gymnasium in the Derbyshire seat of Bolsover, Nigel Farage said The Brexit Party was "going after" Labour MPs who he said had failed to deliver what people voted for in the 2016 referendum.
Great start to our nationwide tour. The gloves are off in this campaign and we are going after Corbyn’s Labour. pic.twitter.com/Ods7tThlZw— Nigel Farage (@Nigel_Farage) November 5, 2019
The Lib Dems and the SNP, who both want the UK to remain in the EU, are also campaigning on the issue on Tuesday.
Stopping Brexit will deliver a £50bn "Remain bonus" for public services over the next five years, Liberal Democrat leader Jo Swinson said.
And SNP leader Nicola Sturgeon will claim that Scottish voters have the chance to escape from the "lost decade" Brexit risks by backing her party.