Labour leader Jeremy Corbyn said there would have to be a "proper vote" on the government's proposals in Parliament, adding: "Here we are, two years since the referendum and the Government still hasn't produced a white paper on its own negotiating stance."
Shadow Brexit Secretary Sir Keir Starmer earlier said Labour had not ruled out the possibility of a second referendum on Brexit.
Mr Bridgen called Mrs May's Brexit pledges "a pretence and charade intended to dupe the electorate".
Mr Rees-Mogg warned that "a very soft Brexit means that we haven't left, we are simply a rule-taker".
A briefing being circulated to the European Research Group (ERG) - a group of Eurosceptic Conservative backbench MPs, which Mr Rees-Mogg leads - says the prime minister's plan "would lead directly to a worst-of-all-worlds black hole Brexit".
The document expresses concern the UK would have to follow EU laws and European Court of Justice rulings and would not be able to develop an "effective international trade policy".
Former Conservative leader Iain Duncan Smith told the Sunday Telegraph if the public perceive Mrs May's plan as "continued membership" of the customs union and single market for goods, the government "will suffer the consequences at the next election".
But Mrs May told the Sunday Times: "The only challenge that needs to be made now is to the European Union to get serious about this, to come round the table and discuss it with us."
She said her plan was a "serious, workable proposal" and when people voted to leave the EU, "they wanted to take control of our money, our laws and our borders and that's exactly what we will do".
The prime minister had gathered her 26 cabinet ministers together at her country residence to resolve differences over the shape of the UK's relations with the EU and break the current deadlock with the EU. The proposals will be published in a white paper next week.