On the subject of the backstop, the PM's spokeswoman said negotiations on it were continuing alongside efforts to agree a future customs model.
The UK's two ports associations are sounding different notes on Britain's post-Brexit customs arrangements with the European Union.
It came as Tory MPs last night warned Mrs May against shackling Britain to the customs union for an extended period after Brexit.
The EU must see any United Kingdom idea "written down in black and white, and we need to know that it's workable and legally operable and we've yet to see anything that remotely approaches that", he said.
May has been struggling to unite her cabinet over the terms of Britain's divorce with the European Union, with a row over future customs arrangement dividing her government and all but stalling Brexit negotiations.
Attending the EU Western Balkans summit in the Bulgarian capital Sofia, the Prime Minister reaffirmed her commitment that there should be no return of a "hard border" between Northern Ireland and the Republic. "It again sounds like trying to have the cake and eat it, like picking what they like, but not the rest", the official said.
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He said: "If we are not making real and substantial progress by June then we need to seriously question whether we're going to have a Withdrawal Agreement at all".
Britain otherwise risks crashing out of the bloc, a scenario that could hurt the economy and disrupt people's lives. "It would certainly help us continue to trade between Britain and Ireland much as we do now".
The EU wants Britain to reveal its preferred option at a European Council meeting in June, but Downing Street has insisted it will not put a time-frame on the process.
The British Ports Association - whose members include ro/ro ports handling over half of all UK-EU trade - is in favor of retaining the benefits of the EU Customs Union in some form.
European Union leaders will assess the Brexit talks' progress next month.