David Davis has said the chances of Britain crashing out of the EU without a trade deal have dropped dramatically as a result of last week’s breakthrough on the principles of a Brexit divorce agreement.

The cabinet minister, who is leading the UK’s negotiations with the EU, said he and Theresa May were seeking a deal that was best described as a “Canada plus plus plus” arrangement.

That meant taking the best elements of deals already struck with countries such as Canada, Japan and South Korea, he said, and adding in services that were key to the British economy.

“The odds of a WTO or no-deal scenario have dropped dramatically,” he said, admitting that he may not have been able to make that statement if last week’s negotiations had ended in deadlock, delaying trade talks until at least March.

Davis also made clear that the promised divorce bill, which is expected to be between £35bn and £39bn, would be paid only once a trading arrangement had been agreed.

“No deal means we won’t be paying the money,” Davis told the BBC’s Andrew Marr Show.

The comments represented a slapdown to the chancellor, Philip Hammond, who claimed just days ago that it was “inconceivable that we as a nation would be walking away from an obligation that we recognised as an obligation”.

The Brexit secretary said the substantive details of a trading arrangement must be in place by March 2019, although he conceded that “some minor negotiations” might continue as the UK entered a transitional period.

He said the deal could not be formally signed until Britain had left the EU, but that it could be done “one minute, or one second after we leave”.

Asked how Britain hoped to achieve its aims of a trade deal in eight months when it had taken Canada many years, Davis reiterated the government’s position that it is easier for the UK given that it already had the same standards as the EU.

He said it was highly significant that the divorce agreement referred to “full alignment”.

“It was changed from no divergence and that’s the point. No divergence would have meant taking cut and paste rules,” he said.

Davis said, however, that full alignment would only affect a few sectors, such as agriculture, road and rail, and would mean the UK achieving certain outcomes but not necessarily in the same way as the EU did.

“We are not looking to create a circumstance where animal welfare is worse in Britain than elsewhere or, safety of food is worse or pollution of waterways,” he said.

Asked about Michael Gove’s suggestion that future governments could take the UK in a different direction with regards to the trade deal, Davis said that was a statement of the obvious.

“Any new government is elected on a mandate of its own. That is a function of democracy. There could be consequences,” he said, admitting that could mean renegotiating elements of a deal.