Under proposals agreed by the other 27 member states, Britain will have no say in its decision-making bodies during the implementation period after Brexit in March 2019.
But it would still have to follow all EU rules and regulations, including freedom of movement and face restrictions on signing off new trade deals.
The terms provoked fury among Brexiteers, with some calling for the Government to reject the EU “ultimatum”.
And the news saw support surge for an online petition demanding the UK makes a clean break in March 2019.
Signatories soared past the 10,000 – the benchmark for an official Government response – and had reached 12,500 by Thursday.
The petition, launched by Leave voter Elizabeth Watson, states: “We must leave the EU completely in March 2019 – no transition period, no delay.
“Theresa May is betraying the British people who voted to leave the EU by making the UK stay in until 2021 and paying billions of pounds to the EU while we stay.
“No immigration control, no border control, no sovereignty – an absolute betrayal of the 17 million voters who chose to leave.”
If the petition hits 100,000 supporters, MPs will be forced to debate it in Parliament.
Critics of the transition deal have included arch-Brexiteer and darling of the Tory membership Jacob Rees-Mogg.
The MP, who leads the European Research Group of Conservatives, has said Britain will be reduced to a “vassal state” of Brussels during the transition.
This week, he called for the Government to “stiffen its backbone” over the approach to a transition period and fall in behind the Brexit blueprint set out by Theresa May.
And he said, despite the approach set out by Mrs May at Lancaster House, the Tory manifesto and the Florence speech, “Government policy seems to be adrift” on the issue.
He said: “If we know where we are going at the end of it, there are many things that Eurosceptics such as me could accept in a genuine implementation with a clear end point that are very troubling if we don’t know the end point.”
Criticising the way Brexit Secretary David Davis has set out the Government’s approach, Mr Rees-Mogg added: “I think it’s important that the Government gets the negotiation of the transition right and slightly stiffens its backbone.”
Mrs May appeared to muddy the waters further on Thursday when she warned the UK would seek to limit the rights of EU citizens who come to Britain during the post-Brexit transition.
Speaking during the second day of her official visit to China, the Prime Minister said those arriving after the Brexit date of March 2019 could not expect to enjoy the same rights as those who came before.
Her intervention provoked an angry response from senior EU figures who insisted EU law, including the free movement of people, must apply throughout the proposed 21-month transitional period.
Guy Verhofstadt, the European Parliament’s co-ordinator on Brexit, said the UK had to remain subject to the entire acquis, the accumulated body of EU legislation and case law, if the transition was to work.
The petition is available to sign online here.