The MPs, who include three former Cabinet ministers, are understood to oppose her proposal to enshrine in law the date of Brexit as 29 March 2019.
Media captionWhat's going on with the EU Withdrawal Bill?
Ms Soubry also hit out at a Daily Telegraph front page labelling her, Mr Lefroy and other prominent Tory critics of the legislation "the Brexit mutineers".
The Telegraph gave over most of its front page to photographs of the 15 backbenchers under the headline: "The Brexit mutineers".
However, Brexit secretary David Davis conceded that even if MPs failed to back that legislation - the withdrawal agreement and implementation bill, Britain would still leave the European Union on March 29, 2019.
But critics warn the European Union withdrawal bill - also known as the repeal bill - represents a power-grab by ministers, while others see the legislation as a chance to shape the prime minister's Brexit policy.
Even ardent Brexiteers quickly sought distance from the paper's coverage with Brexit minister Steve Baker stating that "I regret any media attempts to divide our party" and Dominic Raab signalling his agreement.
GETTYMr Tajani took on the role after former President Martin Schulz stepped down
A series of attempts to rewrite the legislation were seen off with Government majorities ranging from 20 to 266.
"But we want a proper Brexit, one that works for jobs and industry, that's what we're trying to get".
Grieve told MPs that no amount of "arm twisting" would make him vote for the amendment, which was debated but will not be voted upon until next month at the earliest.
Labour's shadow Brexit secretary Sir Keir Starmer said setting a date in law was a "desperate gimmick" that was "about party management, not the national interest".
To that effect, it has tabled its own amendment putting the date of Britain's departure onto the face of the bill, which was being debated later on Tuesday, although not taken to a vote.
He said: "Of course I shall be voting with the government tonight, but I very much hope after this debate - as did not happen after second reading - that the government will go away and think about clause six".
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