On a day where a war of words erupted between EU leaders and Tory politicians, undermining Ms May’s Brexit position, Mr Corbyn penned a letter to the prime minister calling for a number of changes to her approach.
The Labour leader said his priorities, which included being part of the customs union and protecting UK jobs, must be enshrined in the political declaration, setting out future relations with the EU, to win his party’s support.
Mr Corbyn told Ms May that modifications to the Northern Irish backstop would not be enough to win the backing of his party.
In his letter Mr Corbyn calls for a “permanent and comprehensive UK-wide customs union” – a move which is unlikely to get support from Brexiteers in her party.
He states: “This would include alignment with the union customs code, a common external tariff and an agreement on commercial policy that includes a UK say on future EU trade deals.
“We believe that a customs union is necessary to deliver the frictionless trade that our businesses, workers and consumers need, and is the only viable way to ensure there is no hard border on the island of Ireland.”
Downing Street hit back angrily as a range of politicians all spoke about against Mr Tusk’s comments.
The president of the European Council did however repeat the EU position that the withdrawal agreement could not be renegotiated and Jean-Claude Juncker, the European Commission president, echoed the message in a joint statement with Leo Varadkar, saying: “We cannot accept the idea, which is circulating around, that the withdrawal agreement could be reopened.”
Ms May will be meeting with European leaders in the coming days to discuss the withdrawal agreement and in his letter Mr Corbyn said he understood that any negotiation would require “flexibility and compromise”.
Despite the EU’s position of not reopening the negotiations, Mr Corbyn’s letter called on Ms May to secure a number of changes.
“Our first priority must be a deal that is best for jobs, living standards, our communities, in the context of increased and more equitable investment across all regions and nations of the UK,” the letter says.
Labour also want a close alignment with the single market “underpinned by shared institutions and obligations, with clear arrangements for dispute resolution” as well participation in EU agencies and funding programmes. However it notably drops Labour’s previous demand to secure the ”exact same benefits” of the single market.
There are also calls for “unambiguous agreements on the detail of future security arrangements, including access to the European Arrest Warrant and vital shared databases”.
Additional reporting from agencies