However, in an LBC phone-in, mayor of London Khan said he was confident the government will eventually agree a “future relationship” deal as “we need them more than they need us”.
Shortly after Khan’s remarks on Friday, Cabinet Office minister Michael Gove “formally confirmed” the UK won’t seek an extension to the Brexit “transition period”.
It comes after negotiations between the UK and EU stalled following the conclusion of the fourth round of talks last week.
The EU’s chief negotiator, Michel Barnier, even accused Johnson’s administration of seeking to distance itself from agreeing a deal.
Speaking on LBC, Khan, who had been a staunch campaigner for a second referendum, said: “The government thinks the EU needs us more than we need them, but just looking at the numbers in relation to how much we export to the EU, versus how much they export to us, tells me that we need them more than they need us.
“So I’m hoping the government puts aside ideology and dogma and reaches a trade deal with the EU.”
He went on: “I'm confident that we'll do a deal. I think even this government is not that pig-headed.
“The idea that Johnson, [Rishi] Sunak, [Dominic] Raab and [Michael] Gove would go into next year still recovering from COVID-19 – or potentially in the midst of COVID-19 maybe in a second wave – without a deal with the EU would be the worst form of self-harm that this country has ever seen.”
Referring to the economic fallout from the pandemic, Khan added the government has no choice “as we are talking about levels of unemployment not seen since the 1980s”.
The UK, after leaving the EU on 31 January, is currently in a “transition period” in which the two sides have until 31 December to agree their future relationship.
During the transition period, the UK effectively remains a member of the EU. It could have been extended for up to two years, with Downing Street having to give notice of this by 30 June.
Because of the coronavirus crisis, there had been calls for Number 10 to extend the transition period, with leaders primarily focused on the pandemic.
However, Gove fully ruled this out on Friday, saying: “The moment for extension has now passed.”
Johnson, having left chief negotiator David Frost to lead the talks for the UK so far, is expected to take part in fresh negotiations later this month.
There is mounting concern among business – already hit hard by the fallout from the pandemic – at the prospect of a “cliff edge” break to the UK’s remaining access to the EU single market with no new deal to replace it.
Coronavirus: what happened today
Read more about COVID-19
How to get a coronavirus test if you have symptoms
How easing of lockdown rules affects you
In pictures: How UK school classrooms could look in new normal
How public transport could look after lockdown
How our public spaces will change in the future