DIT says that with the agreement the British auto industry, which has consistently warned against a no-deal Brexit, could avoid up to £8m a year in tariff charges on their exports that would apply if the agreement had not been reached.
In the interview Starmer described Mrs May's approach as "reckless" and "blinkered" and blamed her "tunnel vision" for the devastating defeat suffered last month when MPs threw out her Brexit deal by a record 230 votes.
'We know that businesses are leaving the country, we know that businesses are making plans that will damage communities across the country and just this week we had a new chapter in the unfolding nightmare that the trade deals that the United Kingdom businesses enjoy through the European Union will not be ready in time for leaving'.
But a member of May's cabinet pledged Sunday to give parliament a further ballot two weeks later - a measure meant to give the premier more time for talks with the EU.
"We can't allow that to happen", Sir Keir told The Sunday Times. "There needs to be a day when Parliament says that's it, enough is enough".
"What gives certainty is a deal, and that's why we want to see people getting behind us, getting behind this process that we now have", Brokenshire told the BBC.
Demonstrator loses hand at Paris 'yellow vest' march
But last week's official estimates were disputed both by march organisers and an independent estimate carried out for news media. A man was being held for questioning over the blaze, Paris prosecutors said.
The government will give parliament another chance to debate the issue by February 27 using the same format described above, if a deal has not been agreed before then.
May has been seeking changes to the deal with Brussels since it was rejected by a record majority in parliament on January 15.
Labour leader Jeremy Corbyn has written to the Prime Minister setting out five demands that would have to be met for his MPs to support a deal, including a permanent customs union and close alignment with the single market.
But in efforts to build cross-party support for a Brexit deal, she offered flexibility on Corbyn's calls to keep up with European Union measures to protect the environment and workers' rights, asking for further talks with Labour "as soon as possible". The prime minister is now in talks with Brussels to seek these changes to the backstop.
However, the deal does not include financial services - the UK's most valuable asset - as there is no comprehensive agreement between Switzerland and the European Union on financial services.
He underlined that a possible no deal Brexit will mean a "really hard border between the north and south of Ireland, contrary to the Good Friday Agreement".