MPs from all parties are already planning an alliance to defeat Theresa May’s plans for a hard Brexit, just days into the new Parliament.

Strategies to amend future legislation – including a key immigration bill – to force ministers to listen to business groups and to show the EU that Parliament wants a “softer” exit are being drawn up, The Independent has learned.

One Conservative MP said the aim was to give confidence to “bullied” ministers who are reluctant to “speak out”, despite sharing the view that the Prime Minister’s plans put Britain on the road to disaster.

Another MP outlined the importance of convincing Brussels that Parliament can “coordinate” to present a different, more EU-friendly policy to that of the Government.

“It would really show how power has shifted if Parliament can coordinate itself – and that’s not impossible,” the MP said.

Pro-EU Tory Anna Soubry told The Independent: “We are talking to each other and will continue to talk to each other – this is something that transcends normal party political considerations.

“It doesn’t have to be about forcing votes, but it may come to that. Certainly, the threat of losing a vote will weigh very heavily on the Government’s mind.”

Brexit one year on: What happens next?

The threat emerged as Ms May suffered a bruising encounter in Brussels, where the EU torpedoed her “generous offer” on the fate of EU citizens, warning it would make their situation worse.

Some of the MPs want to keep Britain in the EU single market and customs union, although others involved may not be not willing to go that far.

One target will be the Immigration Bill, announced in the Queen’s Speech, because the extent of new controls could be crucial in determining how close Britain can stay to the single market. The Independent, along with Open Britain, has campaigned for Ms May to drop the target of reducing annual net migration to tens of thousands.

Another MP spoke of giving voice to changing public opinion, amid the first evidence that some people who voted Leave a year ago are changing their minds.

Ms Soubry added: “I am up for working with everybody. Hopefully something concrete will come out of it, because this is the most important thing that’s been done in decades.”

She said she was in contact with some of the 34 Labour MPs who, this week, challenged Jeremy Corbyn to change course by fighting to stay in the single market.

Chris Leslie, a former Labour minister, said: “There are discussions informally and my door is always open to MPs from any party, because we have got to put the country first.”

Fellow Labour MP Chuka Umunna MP said: “I know there are many Conservatives, Liberal Democrats and others who reject the Prime Minister’s plan for a chaotic, ideological Brexit, and agree with me that working people will be better off by the UK staying in the single market and customs union.”

Sir Vince Cable, the Liberal Democrat leadership contender, has also spoken of how “tribal differences between the parties have broken down”, as Brexit looms.

"Informally all kinds of networks are being established and I have been sounded out by several of them,” Sir Vince said.

“There are a lot of Conservative MPs who may not have put up a flag called Remain but are very, very worried about the more extreme options on the table and would like to keep either the customs union, or the single market, or both.”

MPs from all parties recognise the greater opportunities for Parliament to wield influence, after the Conservatives lost their majority at the general election.

With no fewer than eight Brexit bills planned, crunch votes loom on future customs arrangements, agriculture and other issues, as well as on immigration controls.

The discussions are tentative until Ms May has passed her Queen’s Speech next week – with the backing of the Democratic Unionist Party, she still expects to do so.

Two former Tory cabinet ministers have also made clear their determination to put together a “sensible cross-party majority” to head off the economic damage from refusing to compromise in the exit talks.

Ken Clarke told the Commons it could “easily command” the future agenda, if MPs put aside party rivalries and worked together.

“Let us show that we can rise above things. I am glad to know that channels are already open to the Liberals and the Labour party – as well as the Scottish National Party, I am sure,” the veteran MP said.

Former Attorney General Dominic Grieve backed him, saying: “If we do not get this right, we will be in very serious trouble. The question is how Parliament goes about ensuring that we come to the right outcome.”

The cross-party challenge presents a further headache for Ms May, after Britain caved in to the EU on its attempt to force an immediate start to talks on future trade.