When asked if that would mean Britain will be outside the EU's common external tariff and therefore able to set its own tariffs, the spokeswoman said: "We will be taking control of our trade policy".
A source familiar with the discussions has told Reuters that Downing Street is considering applying European import tariffs for a time-limited period after December 2020.
At the end of last month, EU's chief Brexit negotiator Michel Barnier said there could be no Brexit withdrawal agreement without the backstop option for the Irish border.
The Irish premier has warned Britain that it must keep some ties to the single market with Brexit in order to avoid a hard border with the Republic.
The idea would be during that period when the United Kingdom would remain aligned with the Customs Union that the United Kingdom could start negotiating trade deals but not actually implementing them. "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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"Earlier, arriving at the Sofia summit, Mr Varadkar said unless there was real and substantial progress" by the time of the next European Union summit in June there would be serious questions as to whether there would be 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 UK authorities will inform Brussels about the willingness to remain in the customs Union of the EU after 2021 due to the unresolved Irish question.
Extending the use of European Union tariffs is part of discussions to make the backstop arrangement more palatable to Britain, and could be triggered if there were a delay in the ratification of the Brexit deal or if there were problems introducing new technology at the border, the source said.
He said it remained an "absolute red line" for Ireland that there must be no hard border on the island and that all 27 remaining European Union states supported the current "backstop" proposal.