European Union leaders will be meeting on the 14 and 15 December as part of the council summit, but numerous deals and agreements announced there will be agreed several weeks in advance, meaning Britain too will need to reach a decision soon on what concessions it is willing to make.
Despite Britain voting to leave the European Union in June 2016, little progress has been made in negotiations, with Brussels refusing to move onto trade until issues such as the Irish border, citizens' rights and the divorce settlement are finalised.
The biggest stumbling bloc remains money.
Brexit minister David Davis said a deal on the border was only possible in the context of talks on future trade and that there can not be any new border inside the United Kingdom as a result, a nod to the Northern Ireland unionists backing his government firmly opposed to the province staying in the customs union.
"While we welcome the language we get from the British government in the context of north-south challenges. there has always been a scepticism on how we are going to get there in the context of the British approach to Brexit as a whole".
Coveney reiterated that if Britain leaves the EU's customs union and does not form some form of new bilateral customs union with the EU, that it is hard to see how London can honor its commitment to avoid any physical border infrastructure.
May faces another test when a key piece of Brexit legislation, the EU Withdrawal Bill, returns to the House of Commons next week.
John Kerr, who drafted Article 50 of the EU's key treaty, said that "while the divorce talks proceed the parties are still married".
Kerr said the British government has misled voters into believing the process is unstoppable.
May warned Friday she would not tolerate attempts "to try to block the democratic wishes of the British people by attempting to slow down or stop our departure from the European Union".
The government says it plans to enshrine in law the date and time of the U.K.'s departure - 11 p.m. on March 29, 2019 - as a protection against delay.