And he warned the Government “has a long way to go before it gets anywhere near” meeting the tests.
His red lines include remaining as close as possible to the bloc’s Single Market and Customs Union, the defence of rights currently provided by the union and “a humane, effective, immigration approach”.
Speaking at a meeting of the Fabian Society today, the former Director of Public Prosecutions said: “If what comes back does not provide for a strong and collaborative relationship we’re not signing it. We’re not voting for it.”
He added the Government’s embarrassing defeat in an amendment vote to its landmark Brexit Bill was proof Labour could muster enough support to challenge the Prime Minister.
In December, MPs voted 309 to 305 in favour of a change to the EU Withdrawal Bill which will allow MPs a “meaningful vote” on the final deal.
Those who voted against the Government included 11 Tory rebels led by former-attorney general Dominic Grieve.
Mr Starmer told the society’s new year conference this afternoon: “We’ve got the two things that matter: one the vote, and two some really strong tests about what we Labour will do when we get to that vote.
“And we will force that vote.”
His other red lines include “a strong and collaborative future relationship” with the EU, effective measures to handle terrorism and national security and a deal which “delivered for all regions and nations of the UK”.
He added: “The way the Government is going at the moment, it has a long way to go before it gets anywhere near our tests.”
The Fabian Society conference was suspended for several minutes earlier today after pro-Trump supporters stormed in during a speech being made by Sadiq Kahn.
The demonstrators held up United States flags and threatened to make a citizen’s arrest of the London mayor, along with Mr Starmer, meeting chair Kate Green MP and Andrew Harrop, general secretary of the Fabian Society.
In footage of the incident, a man can be heard saying: “Ladies and gentlemen, we’re here today to make a non-violent, peaceful citizen’s arrest of those being named.
“They are Sadiq Khan, Keir Starmer, Kate Green MP and Andrew Harrop.
“We stand under common law jurisdiction. If you touch us you will be done for common assault. Do not touch us. We’re not leaving, I’ve paid for a ticket.”
Police eventually led out the campaigners. A spokeswoman for the Fabian Society confirmed to Express.co.uk the speech had been marred by what she described as “far right” protestors.