The zone expanded at the end of August to cover the whole of Greater London, reaching the border of Mr Johnson’s Kent constituency.
A £12.50 daily charge applies for driving in the zone if the vehicle does not meet certain emission standards.
The MP told BBC Radio Kent this week: "This Ulez expansion has nothing to do with pollution. I don't accept what the Mayor of London is saying… This is a cruel form of taxation."
But Mr Khan said Mr Johnson should instead focus on lobbying ministers for a wider scrappage scheme, which could benefit his constituents.
Asked by the Standard about the MP’s bill, the Labour mayor said: “We’ll have to wait and see how this pans out. There’s been court challenges, there’s been all sorts of issues being raised by people.
“The decision to expand the Ulez to outer London was a difficult one, it wasn’t an easy one, but it’s the right thing to do.
“Why? We’ve seen the benefits in central London, with almost a 50 per cent reduction in toxicity, a third fewer children being admitted to hospital with air pollution illnesses. In inner London, a 20 per cent further reduction in toxicity, 500 schools have children breathing cleaner air.
“I think breathing clean air is as important as drinking clean water. I think it’s a right, not a privilege. That’s why I want those in outer London to benefit as well.”
He added: “What this MP should be doing is lobbying the Government for his constituents to get the benefit of a scrappage scheme.
“Every other part of the country, and those living outside those cities, whether it’s Birmingham, Bristol, Manchester, Bournemouth, have benefitted from Government support towards scrappage schemes - his constituents haven’t.
“What he should be doing is standing up to the Government and getting some money for his constituents and London as well.”
The scrappage scheme created by the mayor is only open to those living within Greater London who have non-compliant vehicles. Grants of £2,000 are available for cars and £1,000 for motorbikes, with larger amounts on offer for vans and minibuses.
Private member’s bills normally have little chance of success. But if the Government decides to back them then ministers can find time to get them through the Commons.
Mr Johnson has said he hopes his bill could alter the law by next summer if it is unopposed.
Asked about funding for a wider scrappage scheme, a Government spokesperson has previously said: “At a time when the Government is doing everything it can to support people with the cost of living, it is for the mayor to explain why he thinks it is fair to charge those with non-compliant vehicles £12.50 every time they drive.
“The Government has already provided TfL [Transport for London] with £6bn in funding support since 2020, including almost £102m for projects specifically targeted at helping to tackle pollution.”