Theresa May responded to Jeremy Corbyn's letter with his five demands for a Brexit deal.
The Prime Minister questioned his call for Britain to remain in a customs union with the EU – but welcomed further talks with Labor on a Brexit agreement.
Ms. May wants the two parties to discuss how "alternative arrangements" to the Irish base – a commitment to avoid a hard limit – could work.
She did not reject any of his terms in her response.
In a response to his letter last Wednesday, Ms. May told the Labor Party leader, "It is good to see that we agree that Britain must leave the EU with a deal and that the urgent task is to finding an agreement honors our commitments to the people of Northern Ireland, can mandate support in Parliament and can be negotiated with the EU – not to seek an election or a second referendum. "
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This is the case, in which Mr Corbyn has repeatedly said that there should be parliamentary elections if Mrs May can not reach an agreement by Parliament. Some of his deputies also had the pressure to push for another public vote on Brexit.
However, BBC political correspondent Iain Watson said there are some potential barriers to a deal.
Labor has called for a "permanent and comprehensive customs union in the UK" with the same external tariff. It would give the United Kingdom a say in future trade agreements that the EU might take.
Ms May disagrees and wrote: "I am not sure why you think it would be better to have a say in future EU trade agreements than to be able to do our own business?"
The existing policy statement setting out the objectives for future relations between the UK and the EU "explicitly provides for the benefits of a customs union – no tariffs, fees, fees or quantitative restrictions in all sectors and no control of rules of origin" Said Mrs. May to Mr. Corbyn.
It also recognizes the development of UK's independent trade policy, she added.
Ms May said that smooth trade in goods is "one of our key negotiating goals".
She added: "The basic bargaining challenge is the EU's position that full-fledged trade is only possible if the UK remains in the single market.
"This would mean that freedom of movement is accepted, and the manifesto of Labor's 2017 Labor election has made it clear that you do not support it."
Labor also wants Britain to keep pace with the EU as workers' rights in Europe improve.
While the Prime Minister indicates that existing rights are protected, there will be no automatic update in line with the EU. Instead, Parliament would be asked if it wanted to follow suit each time.
The letter ends with Mrs. May, who said she was looking forward to meeting the two parties "as soon as possible".
The work still has to answer the letter.