The uncompromising stance comes just hours before the prime minister is due to travel to Brussels for face-to-face talks with European Commission chief Ursula von der Leyen.
Their dinner is designed to break the current impasse, as time rapidly runs out to prevent a no-deal Brexit.
Mr Johnson told MPs: "Our friends in the EU are currently insisting that if they pass a new law in the future with which we in this country do not comply or don't follow suit, then they want the automatic right to punish us and to retaliate.
"Secondly, they are saying that the UK should be the only country in the world not to have sovereign control over its fishing waters.
"I don't believe that those are terms that any prime minister of this country should accept."
Mr Johnson also insisted the UK would "prosper mightily" with or without a deal, despite warnings from economic experts.
He was responding to Conservative MP Sir Edward Leigh who reassured him Tory MPs would back him if he returned from Brussels without a deal, “because strength comes with unity”.
Earlier the chances of a no-deal Brexit appeared to rise as cabinet office minister Michael Gove said Mr Johnson would “lay out where movement is required” to rescue any agreement during tonight’s showdown.
In comments similar to Mr Johnson’s, Mr Gove stressed that the EU must ditch its demand that “when the EU changes its rules, the UK has to follow suit or face the consequences”.
“The prime minister has been clear that we are going to maintain high standards in this country, but we are also going to be a sovereign country,” he said.
But Sir Keir Starmer accused the prime minister of being “absolutely stuck and dithering between the deal he knows that we need and the compromise he knows his backbenchers won’t let him do”.
The Labour leader reminded MPs that at the time of the 2019 general election Mr Johnson had claimed that he had “an oven-ready deal” and that the chances of a no-deal outcome were “absolutely zero”.
“The chancellor said in the run-up to the election ‘We won’t need to plan for no-deal because we have a deal’,” said Starmer.
“A year on why should anyone who trusted the prime minister when he said he had a deal, including his chancellor, apparently believe a word that he says now?”
Mr Johnson insisted that when he said he had an “oven-ready deal”, he was not referring to a trade deal, but to last year’s withdrawal agreement, in which he agreed to hand over £30bn to Brussels, guarantee EU citizens’ rights and draw a customs border down the Irish Sea.
Sir Keir responded: “Apparently, get Brexit done just meant the first part of it. The easy bit. I don’t remember that being written on the bulldozer.”
Drawing attention to the decision by Ineos to move car-manufacturing jobs from Wales to France, and to the failure to recruit 50,000 customs agents in time for the end of transition, the Labour leader said: “The prime minister said he had a deal. He didn’t.
“He said he would protect jobs, he didn’t. He said he would prepare for the outcome. He hasn’t.
“Whatever may happen in the next few days. There’s no doubting that his incompetence has held Britain back. So will he end this charade, end the uncertainty, get the deal he promised and allow the country to move on?”
Leaving the single market and customs union without a trade deal would be “a total failure, and it would be the British people who would pay the price,” said the Labour leader.
Mr Johnson attacked the Labour leader for refusing to say whether or not he will whip his MPs to vote for any deal which is reached with Brussels.
Sir Keir retorted: “The prime minister asks me how I’ll vote on a deal he hasn’t even secured. Secure the deal, prime minister.”
Mr Johnson did not respond to Starmer’s demand to say whether he agreed with his own economic forecasters, the Office for Budget Responsibility, who have said that a no-deal Brexit would result in higher unemployment and inflation and a 2 per cent hit to the economy.
He insisted that the UK would remain “a magnet for overseas investment” whether this week’s talks result in a no-deal Brexit - which he refers to as an “Australian solution” because Australia has no trade deal with the EU - or a deal on goods of the kind enjoyed by Canada.
“This country will be ready for whether we have a Canadian or Australian solution,” said Mr Johnson.
“There will be jobs created in this country, throughout the whole of the UK, not just in spite of Brexit but because of Brexit.
“Because this country is going to become a magnet for overseas investment. Indeed it already is and will remain so.”
Mr Johnson added: “Whatever happens from 1 January, this country will be able to get on with our points-based immigration system, which we have put into law in fulfilment of our manifesto commitment.
“We’ll be able to get on with instituting low-tax freeports in places where jobs and growth are most needed around the country. We’ll be able to honour our promises to the British people and institute higher animal welfare standards.
“And we’ll be able to do free trade deals and we’ll get our money back as well.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies