She said: 'We will not accept an agreement that gives the European Union a lock on ending the backstop when we have new customs arrangements in place that meet our commitments on avoiding a hard border for Northern Ireland'.
This is in the best interests of the UK, European Union and Republic of Ireland.
And he said Mrs May's insistence that the arrangement must be time-limited meant that it could not be regarded as a true backstop, providing a fallback option if the UK's preferred permanent solution could not be agreed.
Mr Thompson said the high frequency of transactions meant firms would still have to fill in customs declarations.
While the customs union and hard border issues will create complexity for contract logistics, the report goes on to note: "Ultimately though, what will really matter for contract logistics providers is whether the United Kingdom leaves the single market".
"We are not going to be intimidated by this form of blame game", Barnier told a press conference in Brussels.
"We are just feeling responsible for what we promised in December in our joint report that you will propose the first two options and then, in case there is no option from your side, then we have to be prepared that the Irish border is safe".
Yesterday, Brexit secretary David Davis was, reportedly, threatening to resign over the wording of the government's proposal for a regulatory backstop if London and Brussels fail to strike a deal on the Irish border.
Ms Morrice is a former head of the European Commission in Belfast and was deputy speaker in the Northern Ireland Assembly after it was established in 1998.
Foreign Secretary Boris Johnson has complained that the Irish border issue is dictating "the whole of our agenda" in the UK's Brexit negotiations with the EU.
Others questioned the substance of the proposal. After much toing and froing, the technical document on a "temporary customs arrangement" was published this afternoon (7 June), Catherine Feore looks at what lies within. "How does that fit with the absence of a hard border in all circumstances?"
"There is still an urgent need for clarity on non-customs checks, which account for three quarters of border stoppages. How does that fit with the requirements of our Value-Added Tax system?"
"I've always been clear that this was time-limited and as we've said today [Thursday] the end state at the latest will be in by the end of 2021 and we will be working to ensure that it is in earlier than that".
OMM director Rob Grimmond said: "It is crucial that MPs give due consideration to the offshore renewables industry ahead of their decision on the EU Withdrawal Bill, given the importance of a secure and flexible workforce to the work that we do".
Best for Britain is targeting Labour MPs, but also needs at least 10 Conservative "rebels" if it is to win a vote in Parliament on an amendment calling for a new referendum - which is opposed by both the Conservative and Labour front benches.
After his talks with the prime minister, Mr Davis's chief of staff, Stewart Jackson, claimed victory by posting on Twitter: "Helpful dialogue".