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.”