Liberal Democrat leader Sir Vince Cable has warned that peers across the House of Lords are ready to join forces and inflict defeats on the Government over Brexit.

In an exclusive interview with The Independent, he set out how he has met with peers in a bid to ensure the Government does not use Brexit legislation as an excuse to get rid of rights and protections currently enshrined in European law.

Sir Vince also revealed how interest is growing among members of the Lords in the idea of having a “referendum of the facts” once the country knows what kind of Brexit deal it faces.

His intervention follows a further round of Brexit talks which again failed to move negotiations forward and comes as Theresa May’s ministers begin a drive to push through their key piece of legislation necessary to make EU withdrawal happen.

But while Ms May has a good chance of winning votes on her bill in the House of Commons with the Northern Irish DUP’s backing, she is weaker in the Lords against opposition from the Lib Dems, Labour, Tory rebels and crossbench peers.

Sir Vince explained: “Our people are fairly optimistic that on amendments of substance, particularly where this involves the rights of Parliament, the ‘Henry VIII powers’, they will be able to defeat the Government.”

Brexit: the deciders Show all 8 1 /8 Brexit: the deciders Brexit: the deciders European Union's chief Brexit negotiator, Michel Barnier Getty Brexit: the deciders French President Emmanuel Macron Getty Brexit: the deciders German Chancellor Angela Merkel Reuters Brexit: the deciders Commission President Jean-Claude Juncker EPA Brexit: the deciders The European Parliament's chief Brexit negotiator Guy Verhofstadt Getty Brexit: the deciders Britain's Prime Minister Theresa May Getty Images Brexit: the deciders Britain's Chancellor of the Exchequer, Philip Hammond PA Brexit: the deciders After the first and second appointed Brexit secretaries resigned (David Davis and Dominic Raab respectively), Stephen Barclay is currently heading up the position PA

The EU (Withdrawal) Bill coming to the Commons next week hands sweeping powers to ministers to change legislation, so they can rewrite laws affecting the UK which up to now have been enshrined in Brussels, but after Brexit will be written in to British statute.

Campaigners fear that it will be used as an opportunity by Conservative ministers to hollow out employment, environmental and equality protections and human rights laws.

Sir Vince went on: “[The Lib Dems] have clout in the Lords, if we are able to combine with other groups. We are talking to the crossbench group, I spoke to them last week and there must have been 50 or 60 of them in the room.

“These are serious people – Lord Kerr, the man who negotiated the original treaty [containing Article 50], and former heads of civil service, serious lawyers. Many of them are in the same position that we are.

“So we can work with a number of crossbenchers, and Labour and Conservative rebels have less to lose in the House of Lords than they do [in the Commons].”

On Friday crossbench peer Lord Kerr accused Ms May of failing to tell the public that Brexit is easily reversible, and that the UK can unilaterally stop it if it wishes.

Vince Cable's party conference speech in 60 seconds

He called on the Prime Minister to release legal advice so far suppressed, which is expected to show that there is nothing in Article 50 stopping ministers from ending the Brexit process.

Sir Vince said that almost all the questions he was asked at the meeting of crossbench peers, which included Lord Kerr, were about the possibility of another referendum.

He said: “Hitherto I think most of them had said ‘forget it’. But they are beginning to realise that it is a very important potential mechanism.

“They were asking about the basic reasoning behind it, how it would work, what the question would be – it needs legal drafting, but the question would be do you … wish to accept Brexit as offered by the current government, or do you wish an exit from Brexit and to remain a full member of the European Union?”

Theresa May needs to move Brexit talks on in December (Getty)

Sir Vince said he now puts the chances of Brexit falling through as “maybe 20 per cent, possibly 25 per cent”, having put the chances far lower earlier in the year.

He added: “The probabilities of having an exit from Brexit are rising because of the chronic weakness of the Government – the lack of ability to negotiate a satisfactory deal.

“We will almost certainly be faced with a poor deal, maybe no deal at all and I think under those circumstances, large numbers of, initially MPs, and then the public, wanting to revisit the basic question will rise.”

His forecast comes after another round of difficult Brexit talks failed to see the two sides moving towards the point where talks can progress to transition and trade.

EU chief negotiator: UK has two weeks to agree Brexit 'divorce' bill or no trade talks this year

Chief EU negotiator Michel Barnier gave the UK two weeks to set out how it would meet its financial obligations to Brussels on withdrawal, the so-called “divorce bill”.

A failure to do so, he indicated, would mean the next European Council in December would not give approval to move talks forward – a failure that could destabilise Ms May’s Government and lead to growing calls from Tory Eurosceptics for the UK to abandon talks altogether.

The Independent understands Ms May is planning to go over Mr Barnier’s head and appeal directly to European capitals for talks to move forward before Christmas.

Recent BMG Research polling for The Independent showed that 76 per cent of people felt negotiations with Europe were going either “very” or “quite” badly, just 12 per cent thought they were going “very” or “quite” well and 12 per cent did not know.