The attack comes as it emerged the Prime Minister will meet with the Cabinet on Wednesday to discuss her plans for Brexit.
Ministers will gather at the Prime Minister's country retreat of Chequers to discuss the next steps in the process amid speculation that Mrs May will implement Article 50 - triggering the two-year period leading to Brexit - without seeking the backing of Parliament.
A Downing Street source confirmed Brexit was "top of the in tray" for Mrs May as she begins her first full week back at work in Westminster after her summer holiday in Switzerland.
There has been much speculation over whether parliament would be given a vote on the issue, with lawyers and politicians in disagreement over whether the Prime Minister has the authority to trigger Article 50 and begin the process of withdrawing from the European Union without parliament’s approval.
The referendum itself was advisory, and not legally binding, but the legislation that was passed in order to hold it didn’t state whether a decision to leave would need parliament’s backing.
It has been reported that government lawyers have advised the Prime Minister the procedure could be begun without a vote, but she could still face legal challenges were she to do so. 480 of parliament’s 650 MPs favoured remaining in the European Union, but overturning the result of the referendum would be a dramatic step.
Labour leadership candidate Owen Smith said the Prime Minister was “running scared”.
“Theresa May is clearly running scared from parliamentary scrutiny of her Brexit negotiations,” he said. “She’s looked at the numbers and she knows she might not win a vote in parliament.
“She hasn’t set out what Brexit means and she doesn’t want to be held to account on vital issues such as stripping away workers’ rights and environmental safeguards.”
Mr Smith has said that the British public have not voted on the terms of any post-Brexit deal, which remain unknown. If he was to become the opposition leader, he would, he said, “press for whatever final deal she, Boris Johnson, Liam Fox and David Davis come up with” to be put to the British people, either in a second referendum or at a general election.
Labour’s shadow international trade secretary Barry Gardiner also challenged the lawyers’ advice. “The logic of saying the prime minister can trigger article 50 without first setting out to parliament the terms and basis upon which her government seeks to negotiate – indeed, without even indicating the red lines she will seek to protect – would be to diminish parliament and assume the arrogant powers of a Tudor monarch,” he said.
“Parliament cannot be sidelined from the greatest constitutional change our country has debated in 40 years.”
The prominent Eurosceptic MP Bill Cash told the Telegraph any decision not to hold a vote would be "what the people wanted to hear".
“There are people who are threatening to try and stop Brexit. The bottom line is that there is nothing that could possibly be allowed to stand in its way. Everyone in Europe is expecting it, the decision has been taken by the British people, and that’s it. Let’s get on with it," he said.