She said the government needed to "get serious" about policy on a customs union and guarantee to "legislate for the protections around workers' rights".
"The idea that you can have a customs union with the EU and at the same time, as an outside country, have an effect on EU trade policy, is to not understand the EU treaties".
"I think it must be pretty obvious that if you are going to have a time limit to the backstop, and I think that would be a very good thing, it's got to fall before the next election".
Theresa May has said she will not allow Britain to be part of the Customs Union after Brexit following a backlash by Eurosceptic MPs and ministers.
The Leave campaign figurehead was speaking as Brexit Secretary Stephen Barclay prepared for talks with European Union chief negotiator Michel Barnier as the Government stepped up efforts to secure changes to the backstop, which is created to keep the Irish border open after the UK's withdrawal.
Asked if changes to the backstop proposals could come in a separate codicil to the Withdrawal Agreement, Mr Johnson said: "I don't think that would be good enough".
"I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deal?"
It also follows an exchange of letters between Mrs May and Labour leader Jeremy Corbyn.
BAFTA 2019: Kate Middleton, Vision In White, Sparkles In Princess Diana's Earrings
Kate Middleton has several pieces of jewellery from Princes Diana's collection, which she uses every now and then. This isn't about freedom of speech. "Enough is enough.
She also questioned whether the call for completely "frictionless" trade would mean reneging on Labour's commitment to end free movement by requiring single market membership.
Treasury Chief Secretary Liz Truss refused to rule out resigning if Mrs May backed a customs union.
Barnier told a news conference in Luxembourg that time was "extremely short" to conclude a deal before Britain is due to leave the bloc on March 29.
Ministers have conceded in private meetings with business leaders that they will not be able to replace all of the deals before the Brexit deadline on 29 March, meaning a large proportion of United Kingdom exports could shift to World Trade Organization rules.
She'll say that if she hasn't brought them new deal by February 27, there will then be another opportunity to vote, Communities Secretary James Brokenshire confirmed in an interview.
British lawmakers overwhelmingly rejected the deal, agreed in November, in a vote last month, leaving Britain on course for an abrupt Brexit with no transition period to minimise expected economic disruption.
Last month, the Parliament approved an amendment that supported most of the deal but called for backstop - a last-resort option to prevent a hard border in Ireland to be replaced with "alternative arrangements".
Mrs May is to give a statement to Parliament on Tuesday, a day earlier than planned.
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