* EU 27 give Barnier mandate for transition talks with London
* Ministers warn Britain on outstanding divorce issues
* See no chance of British vote in EU during transition
BRUSSELS, Jan 29 (Reuters) - European Union ministers warned Britain on Monday not to fall behind on outstanding divorce matters as they gave their negotiator the mandate for parallel talks with London on the post-Brexit transition.
Britain is set to leave the EU in March 2019 and the remaining 27 member states have now prepared their joint stance on what they expect of London during a transition period until the end of 2020.
"It will be the full EU acqui (legal framework) in the UK to be applied, without participation in (EU) institutions and the decision-making process as the UK will be a third country after the withdrawal date," said Foreign Minister Ekaterina Zaharieva of Bulgaria, which holds the bloc's rotating presidency.
EU Brexit negotiator Michel Barnier can start talks with London on the transition immediately and his deputy highlighted the unity of the 27 by saying they endorsed the document "within two minutes".
But ministers also warned London should not take for granted the settlement of Britain's divorce package with the EU, with outstanding issues involving the EU nuclear agency Euratom, customs arrangements, and protection of personal data.
The EU said in December that "sufficient progress" was made in the divorce talks to launch parallel transition negotiations.
But it says they can go on only as long as London swiftly puts what has already been agreed into legal texts, especially on safeguarding the rights of some three million EU citizens in Britain, and on the Irish border conundrum.
NO VOTE FOR BRITAIN
"Before Christmas there was an agreement that ... there would be full regulatory alignment on the island of Ireland," said Helen McEntee, Ireland's minister of state for EU affairs. "We're obviously keen to see what that will look like."
Britain has said it wants out of the EU's single market and customs union while keeping an open border between its province of Northern Ireland and the Irish Republic, an apparent contradiction that has yet to be fully addressed.
While the bloc is open in principle to extending Britain's transition period, the ministers made clear they did not want to get stuck in protracted trade negotiations to fix London's future relationship with the bloc.
"I don't think that there is any good thing in having a too-prolonged transition arrangement. I think it's very important that we come to a new agreement as soon as possible," said Sweden's EU affairs minister, Ann Linde.
British Prime Minister Theresa May has come under fire over her Brexit strategy again in recent days, with eurosceptic rivals criticising her for largely accepting the EU push to for a status quo transition.
Asked if London could have more say during the transition, Italy's Sandro Gozzi said: "I think it is rather difficult... If you leave, you leave."
"If you decided democratically to get out of the decision-making process, as Britain decided to do with (its 2016) referendum, then you can't be in the decision-making process," said Gozzi.
"The sooner the Brits are clear about the future, it would be better for everyone... The more the transition is similar to the current situation, the better for everybody. We have to use our time and energy not in shaping the transition but in shaping the future relationship." (Additional reporting by Robert-Jan Bartunek, Samantha Koester, Philip Blenkinsop and Alastair Macdonald; editing by Mark Heinrich)