The Foreign Secretary has said the UK should not have to abide by any new EU rules during the transition period, and that Britain should not make payments to Brussels after it.
Some senior Conservatives, meanwhile, have said Britain should walk away from Brexit negotiations by Christmas if no serious progress is being made.
Mr Johnson told the Sun newspaper there can be "no monkeying around" about withdrawal from the EU.
The move came as a letter to the Prime Minister from senior pro-Brexit Tory MPs and business figures in the Leave Means Leave group stated: "If the EU is not seriously negotiating a free trade deal by Christmas 2017, the Government should give formal notice that we will move to World Trade Organisation rules in March 2019."
Signatories calling for the hardline stance include former Brexit minister David Jones, and the issue is set to feature heavily at the Tory conference.
However, Scottish Tory leader Ruth Davidson called for "serious people" to take charge of Brexit process.
The interventions came as Mrs May is attempting to assert her grip on her party ahead of its annual gathering.
As the party faithful converge on Manchester, the Prime Minister insisted Labour was "unfit to govern" as she pledged to listen to the concerns of young voters after the Tories lost their Commons majority in the snap general election in June.
Mrs May said: "As Conservatives, we have a vision of a country that works for everyone, not just the privileged few - precisely the direction I set when I became Prime Minister last year.
"I understand the concerns raised, particularly by young people, during what was a disappointing election for my party.
"So my determination to act on those concerns, and crucially, to fulfil the promise of my first speech on the steps of Downing Street, is greater than ever."
Mrs May added that the conference would see the party "setting out our road to a better future for you and your family".
She said: "Yes, we have to get the best Brexit deal - but we must also take action here at home to make this a fairer place to live for ordinary working people.
"The social contract in our country is that the next generation should always have it better than the last.
"Conservatives have a plan to make that a reality."
With most polls putting the Tories and Labour neck and neck, Mrs May said a vote for Jeremy Corbyn as prime minister was too risky.
Liberal Democrat leader Sir Vince Cable said Mr Johnson's intervention had undermined the Government's Brexit negotiating position.
"Boris Johnson's latest red line sends an appalling signal to EU negotiators who thought they were dealing with David Davis and Theresa May but now realise that the strings are being pulled by others," he said.
"Senior Conservatives are displaying an abject failure to act together in the national interest and seem more motivated by selfish, personal ambition."
Mr Corbyn said the Foreign Secretary's stance threatened a trade war with the EU.
He said: "It seems a pretty dysfunctional Government. I can't imagine what it's like sitting around a table with their Brexit negotiating team because there are three or four people with three or four completely different opinions.
"Boris this morning seems to be saying two years maximum on the transition period and then no shadowing of EU rules. Well, that sounds to me like a threat to have a trade policy that undermines Europe.
"Therein lies the basis of a trade war of the future, therein lies a threat to thousands and thousands of jobs in Britain.
"You have got to have a serious, adult, grown-up relationship with Europe."