Prime Minister Theresa May has consistently rejected such a deal.
As a result, the finer details on the party's position regarding Brexit were absent and leaves some questions.
So what would the government like? If Labour turns its back on good collaboration between the Government and the private sector - putting vital sectors exclusively in the hands of politicians - public services, infrastructure and taxpayers will ultimately pay the price.
While the Conservative government has reportedly told senior bankers it will put financial services at the heart of a new European Union trade deal, however, Corbyn's speech today implied that banks could be left in the cold if Labour is elected.
What it means: Labour's backing the United Kingdom forming a new trading relationship - called a customs union - with Europe after it leaves the EU, and keeping all the protections over things like the environment and workers' rights. I imagine in private the leadership would like to be outside the EU, Single Market and Customs Union but are having to bow to huge pressures within the Parliamentary Party in order to maintain unity.
The change in Labour policy comes as Tory remainers prepare to rebel to force the Government to sign up to a customs union.
In his landmark Brexit speech on Monday, Jeremy Corbyn announced that Labour would seek to keep Britain in a Customs Union with the EU after Brexit and, in doing so, be "internationalist". "We want to have the freedom to sign our own trade deals and to reach out into the world", he said.
"As yet, no new Nuclear Co-operation Agreements (NCAs) have been signed, discussions for a new trading arrangement with the European Union have not begun, an agreement on continued involvement in nuclear research and development has not yet been reached and without a transitional period and continued relationship with Euratom, a new safeguarding inspections regime will need to both be agreed and capable of implementation by March 2019 - something the Office of Nuclear Regulation has stated it would not be able to deliver".
"Labour would not countenance a deal that left Britain as a passive recipient of rules decided elsewhere by others".
"The Government will not be joining a customs union". Thus, the needs of British industry will be at the mercy of French farmers, German manufacturers, Spanish fishermen and every other Tom. There is also the fact that membership of both would effectively equate to full membership of the EU. It's never been entirely clear what a job first Brexit is, or what's been meant by access to the single market. Retaining our place in the Single Market would avoid that. "This is even more central to economic opportunities and prosperity".
The pro-European Liberal Democrats want to stay in the Brussels club, despite acknowledging its imperfections.
The former UKIP leader and vocal Brexit advocate was appearing on Channel 5's "The Wright Stuff", when he said that only another vote would silence "moaning" politicians and critics - and finally draw a line under the UK's withdrawal from the European Union. Denying us that right would be a scandalous betrayal of those who voted to leave the EU. Importantly, a porous border with the Republic of Ireland is still not guaranteed.
In addition to its implications for trade, leaving the customs union would complicate the issue of the Irish border.
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