"We are in constant contact on these issues with the Government and during our discussions, we reiterated that United Kingdom-Republic of Ireland arrangements may be necessary as we exit the European Union", she said.
"We do not now see how it will be possible to reconcile there being no border with the Government's policy of leaving the Single Market and the Customs Union, which will inevitably make the border between Northern Ireland and the Republic of Ireland the EU's customs border with the United Kingdom".
Theresa May's plan for a "light-touch" border using technology is "untested and to some extent speculative", its report added.
Avoiding a so-called "hard border" on the island of Ireland is the last major hurdle before Brexit talks can move to negotiations on Britain's future trade relationship with the European Union and a possible two-year Brexit transition deal.
Open access will have to end when Britain leaves the single market and customs union, the Commons exiting the EU committee said.
Kate Hoey with Nigel Farage in London during the EU referendum campaign
Now the Republic of Ireland is a member of the European Union, Northern Ireland is a bona fide member of the United Kingdom, hence it is the responsibility of the EU (not Britain's) to address any Irish border problem (real or imaginary?) that one of its members foresees.
Mentioning British Prime Minister Theresa May's request that a final offer is put on the table by December 4, Tusk added that after that: "We can assess whether sufficient progress can be made at the upcoming European Council".
Expressing full support to Varadkar, Tusk said: "The key to the U.K.'s future lies in Dublin", and the other member states would back whatever Ireland decides.
"If there is any hint that in order to placate Dublin and the European Union they're prepared to have Northern Ireland treated differently to the rest of the United Kingdom, then they can't rely on our vote", DUP member of parliament Sammy Wilson said in an interview with the BBC.More news: Aaron Boone's bond with the Yankees goes beyond one home run