Accusing the prime minister of attempting to “railroad” MPs in the Commons into passing her deal, he said Ms May was presenting a “false choice” between her negotiations, or no deal at all.
It follows reports that multiple Labour MPs are prepared to support Ms May's Brexit agreement if the alternative is Britain crashing out of the bloc - even if Jeremy Corbyn orders his party to vote against the Tories' deal.
But Mr Khan, who has in recent weeks thrown his support behind a fresh referendum on any Brexit deal, said the government was engaging in a “brazen attempt to blackmail MPs into voting for a bad Brexit deal”.
“This is a totally false choice - there are still a wide range of options on the table that would allow us to fix the chaotic mess that the prime minister has made of the negotiations,” the London mayor told ITV's Peston on Wednesday evening.
He continued: “History will judge our parliamentarians on this issue like few before. This will be seen as one the biggest, high-stake parliamentary votes in our history - similar to the vote on the Iraq war.
“MPs must think carefully about how they want to be remembered. And the real question is this: whose side are you on? And the answer must be” we should all be on the side of the next generation.“
Mr Khan's remarks came as Ms May appeared to be granted a temporary reprieve from her parliamentary party after addressing MPs at the 1922 Committee of backbench Tories in Westminster.
The meeting followed mounting speculation that the chair of the committee, Sir Graham Brady, had received close to the 48 letters required to hold a vote of no-confidence in the prime minister.
But speaking after the gathering of Tory MPs, the former home secretary, Amber Rudd, said Ms May has addressed her colleagues with “passion and emotion”, and said she believed the prime minister was safe in the job.
Ms Rudd praised the PM, adding: "She got a warm welcome, she talked quite emotionally about why she was doing this for the good of the country and how it was important that the public and our party members realise that we are behind her and that we all wanted the same thing - which is to lead in the best interests of the country."
The Conservative MP Michael Farbricant also described the meeting as a “love in”, telling journalists gathered outside the meeting room: “It wasn't Daniella in the lions' den, it was a petting zoo.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies