A weakened May, her authority shredded by successive defeats, said her Conservative lawmakers would get a free vote, rather than having to follow a party line.
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He added he considered it unlikely that May would test the deal she managed to get from the European Union with a third vote, saying that doing so would be "completely crazy" for the British government.
Hours before a vote on the deal in parliament, May had failed to win over the main Brexit faction in her own party, while Northern Ireland's Democratic Unionist Party (DUP), which props up her minority government, said it would vote against her.
It said: "To prevent unfair treatment of Northern Ireland businesses, goods arriving from Ireland would still be subject to the same VAT and Excise duty as today and the and the United Kingdom government would continue to collect these taxes on Irish goods in future".
Now, her ability to negotiate the course of Brexit has mostly been handed to Parliament, who will determine the course by its votes this week.
But May's entreaty fell on deaf ears among lawmakers whose support she needs.
The government insists that this will not create a border down the Irish Sea, as there will be no checks on goods moving between Northern Ireland and Great Britain.
Opinion polls show that the British public will stomach a short delay to Brexit, but support drops away markedly the longer the extension is.
Supporters of Brexit say while the UK leaving the European Union bloc might bring some short-term instability, in the longer term it will allow the United Kingdom to thrive and also enable the European Union to pursue a policy of deeper integration which the UK was vetoing. And no indication that Britain is any closer to knowing what it wants from Brexit.
The tariffs, meant to be temporary, wouldn't apply to goods crossing from Ireland to Northern Ireland, raising fears the plan would fuel smuggling across the border. However, the text of the 585-page withdrawal agreement remained unchanged.
Renegotiated late Monday night, the latest version of the deal was defeated by 391 votes to 242.
Earlier, Brexiteers seized on new legal advice from the Attorney General Geoffrey Cox, which confirmed that Britain could still be trapped in the arrangement for years after it had formally left the 28-nation bloc.
"Now is the time to come together to back this improved Brexit deal and deliver on the instruction of the British people", May said.
"Let me be clear: the only legal basis for a transition is the WA".
"If we leave without a deal, we will set the majority of our import tariffs to zero, whilst maintaining tariffs for the most sensitive industries".
But the rest of the EU is reluctant to postpone Brexit beyond the late May elections for the EU's legislature, the European Parliament. "There is no alternative".
A spokesperson for European Council President Donald Tusk said MPs second rejection of the agreed withdrawal plan "significantly increased" the risk of a "no-deal" divorce.
"Politicians should be under no illusion: this package of mitigating measures do not help make the case for no deal". It is what you do with this second chance that counts.
"If you pushed me to the end point where it's a choice between no deal and no Brexit ..."
Proposed tariff rates on a range of food products were announced as a proportion of the so-called "most favoured nation" (MFN) now imposed by the European Union on imports from countries which do not have a free trade agreement.