"We welcome the government's commitment to negotiating an interim period so that firms can ensure they are ready to adapt to the changing relationships and thrive under the new partnership being created with the European Union", it adds.
The leaked Home Office immigration paper published by the Guardian on Tuesday pointed to firmer controls on freedom of movement immediately on Brexit, raising concerns about whether the EU27 would be willing to negotiate a transition deal that maintained many aspects of the single market, as the government appears to hope.
The MPs' letter has been obtained by BBC political editor Laura Kuenssberg, who says it is created to send a message to ministers "not to soften the government's plans".
But the move by the backbench caucus, which coordinates parliamentary tactics and funds research backing a hard Brexit, was widely regarded at Westminster as a show of strength, after a summer in which opinion in the cabinet had appeared to be shifting towards a closer relationship with the European Union after March 2019.
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She missed a meeting with a client Friday afternoon, and her uncle Jeff Walters reported her as a missing person Saturday. Floodwaters and rain hampered the pursuit, yet experts followed her cellphone to a Baytown, Texas bog.
She said: "I think one of the things the United Kingdom government didn't do that they should have done was pitch-roll this: remind the British public that when it comes to European negotiations - and we've had several decades of them - we are told no until five past midnight and then suddenly a deal gets done in the wee small hours of the morning".
"Continued membership of the single market, even as part of a transitional arrangement, would quite simply mean European Union membership by another name - and we can not allow our country to be kept in the European Union by stealth".
But the row over the details of any transition deal has also been fought out in the cabinet, with Philip Hammond, the chancellor, leading the charge for a prolonged transition to allow businesses time to adjust and prevent a so-called "cliff edge".
But the message sparked fury from pro-EU Conservatives, who said it went beyond government policy.
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Rattled by the test, South Korea on Tuesday conducted live-fire exercises at sea in its second straight day of military display. South Korea's navy is planning a feasibility study over getting such vessels, although some experts see the possibility as low.
A spokesman for British Prime Minister Theresa May declined to comment but said there had been lots of engagement with companies over Brexit.
United Kingdom businesses are increasingly concerned that moves to leave the single market and customs union would damage their operations.
The Hansard Society thinktank also criticised the bill, saying clause 17 in particular, which was condemned by Keir Starmer, would "hand the government a legislative blank cheque".
Sky News television, which first reported the letter earlier Wednesday, said company chiefs expressed incredulity at being asked to sign.
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Earlier, Prime Minister Narendra Modi had also met the crew and had extended his best wishes for the mission. Air Chief Marshal B S Dhanoa was also present at the base.
Damian Green, May's de facto deputy, also sounded a conciliatory note on Thursday. "It's very important the bill will get passed", he told Radio 4's Today programme.