Transport Secretary Grant Shapps said he had spoken to Mr Khan about ensuring there is "enough space to be safe" on London Underground trains for those who must travel, and offered the support of his department.
But with many businesses remaining open for their staff and key healthcare workers in the United Kingdom capital needing to use the TfL network to travel to work, commuters have been forced to stand close to each other on packed trains exposing themselves to greater risk of contracting the virus.
London tubes are running a reduced service during the lockdown.
She told the PA news agency: "Seats on the train all had at least one person so people needed to stand, and the District line was busy as well". I still don't think things are improved as a large amount of people are commuting early in the morning. "As we work through these issues with our supply chain, consideration will be given to the impact on workers, particularly those who are on low incomes". The choice isn't there and my commute is quite long.
Mr Khan demanded employers enable their staff to work from home "unless it's absolutely necessary". "Ignoring these rules means more lives lost".
She added: "I feel like I am risking my health trying to get to work".
London transport commissioner Mike Brown said: 'The Government and the Mayor have given clear instructions to stay safe and to stop travelling in all cases other than critical workers making absolutely essential journeys. Although the mayor Sadiq Khan stressed that public transportation should only be used for transportation of key personnel. Transport workers and other staff are risking their safety.
An NHS worker has urgently called for immediate action by the government to remedy the situation across the London Underground network.
With suppliers themselves also cutting back of deliveries to building sites, a suspension of engineering works on TfL and shutting construction sites on Crossrail was more a matter of when rather than if.
A medical expert said last week, for every death there are most likely thousands of people in the capital that have coronavirus.