MEPs say that the fundamental principles of the EU — the free movement of people, goods, services and capital — must not be compromised in any final agreement on Britain's exit from the bloc and its new relationship with the remaining 27 member states.
"We will be sorry to see the UK go. However, the decision of one member to leave should not put all of Europe's shared achievements at risk. We will not allow Brexit to undermine the basic principles that bind the EU. Prime Minister May must once again be reminded that any privileged access to the single market must go hand in hand with freedom of movement," said the Greens/European Free Alliance (EFA) co-president Ska Keller.
"We will not accept anything that degrades the existing rights of European citizens. The status of British citizens living in the EU, and people from across Europe living in the UK, must be an urgent priority for the negotiations. They must be able to continue to live and work in the countries in which they have made their homes. Even if the UK is now leaving the Union, the close ties between the British and EU citizens will persist. It is of key importance that programs like Erasmus can continue to bring young people together," she said.
"For the Socialists and Democrats (S&D) Group it is clear that the four freedoms of the single market are indivisible. Theresa May can forget about an arrangement that alters this. This is a red line for us. We will not allow a future relationship that damages the integrity of the single market or lowers European legal, social, environmental and health standards," the S&D party said in a statement.
"We want to ensure an orderly Brexit. We want the negotiations to be fair, the future relationship with UK to be balanced and comprehensive and the United Kingdom to remain a close political and economic partner to the EU," the S&D said.
"We deeply regret that the UK will be leaving us. With such a rich shared history, the UK will always have a special relationship with the EU. We want, as far as it is possible, to accommodate the wishes of all UK citizens, not just those who voted to leave," said co-president of the Greens/EFA group in the European Parliament, Philippe Lamberts.
"This makes the close involvement of the devolved powers of Northern Ireland, Scotland and Wales essential to successful negotiations. We also want to reflect the wishes of young people, so many of whom voted to remain part of the European family.
"On trade, we have a clear shared interest. However, while we are not looking to punish the UK or settle scores, it must be clear that they cannot hope to get a better deal outside the EU than in it," Lamberts said.