Peers should "not throw in the towel early" over Brexit, Peter Mandelson has said as he warned ministers they face defeats over key negotiating principles.

The Labour former cabinet minister believes the Lords will force changes to legislation intended to allow Prime Minister Theresa May to have the power to start the formal two-year Brexit process.

He insisted there is a "strong body of opinion" among peers over guaranteeing the future of EU nationals living in the UK and in giving Parliament a vote on the final Brexit deal in which the Government could be sent back to negotiate a better arrangement.

Ex-EU commissioner Lord Mandelson added the House of Commons "must prevail" on the European Union (Notification of Withdrawal) Bill as he also cautioned against a "Brexit at all costs".

His comments came after Conservative former minister Dominic Raab urged peers with generous EU pension pots to ensure they "came clean" and declared these when speaking in Parliament on Brexit.

Two days of debate on the Bill in the Lords will occur on Monday and Tuesday before amendments are considered the following week.

The Government lacks a majority in the Lords, with 252 Conservatives among the 805 peers - giving the opposition and independent crossbenchers a chance to inflict defeats.

MPs approved the draft legislation unamended and with an overwhelming majority earlier this month as Mrs May seeks to start Brexit talks before the end of March.

Asked if his view was that the Government could be defeated over the issues of EU nationals and how Parliament votes on the final deal, Lord Mandelson told BBC One's Andrew Marr Show: "I think it is.

"I think there's a strong body of opinion, across party and amongst the independent peers as well, that both these issues are very serious.

"But of course when it comes to EU citizens, the British Government is not negotiating with itself and there will be people among the member states who say 'No, we don't want to take this issue now, we'll take it later on during the course of the negotiations' - because it's as much a negotiating gambit for them as it is for Britain."

Questioned if there will be a long parliamentary battle between the Commons and Lords over the Bill, Lord Mandelson said: "At the end of the day, the House of Commons must prevail because it is the elected chamber.

"But I hope the House of Lords will not throw in the towel early."

Pro-EU Lord Mandelson, referring to the outcome of the Brexit talks, said: "We're going to have less trade, we're going to be paying through the nose for it and, broadly speaking, we're going to have the same number of immigrants coming to the country as well.

"Is that a reasonable deal? Don't you think the public will have something to say about that outcome when the negotiation ends? I think they will."

He also claimed: "There is no trade agreement in the world that will give us the same benefits in trade that we have now if we were to follow the Government's Brexit at all costs negotiation."

Justice Secretary Liz Truss said Lord Mandelson was a "blast from the past" and needed to move on from the referendum result.

She added that peers should "recognise the will of the people" and the "overwhelming" vote for the legislation in the House of Commons.

She told the same programme: "I just listened to Peter Mandelson, it was like the referendum had never happened.

"He seemed to be making the same argument that was being made last year and which the British people rejected.

"He needs to move on, and the Labour Party need to move on, because we are now in a new reality. He is a blast from the past, frankly."

She added: "The fact is it's a simple Bill on 'do we trigger Article 50'. The British people voted for that, they were clear in the referendum and the House of Lords now needs to get on with it."

Pressed on whether the Parliament Act would be used to force through the legislation if peers delayed it, she said: "I fully expect the House of Lords will recognise the will of the people and the will of the House of Commons, which was overwhelming, to pass that legislation."

Ms Truss said her understanding of Article 50 was that it was "irrevocable" and, despite supporting Remain in the referendum, if there was a second public vote "I would vote for out, because it's the settled will of the British people".

Around three million EU citizens are waiting to find out if they can remain in the UK, along with more than a million British citizens in other EU member states, following last June's EU referendum.

The Observer reported a leaked document drawn up by MEPs on the European Parliament's employment committee to aid Brexit negotiations warns it would be difficult to determine which EU citizens were residing legally in the UK before Brexit takes effect.

The newspaper reported that the document stated: "If all 3.3 million EU citizens were to initiate procedures aimed at proving the 'exercise of treaty rights' the administrative system would be overburdened."

A Home Office spokesman said securing the status of EU nationals and British expats is a "priority" as soon as Brexit negotiations begin, adding: "The rights of EU nationals living in the UK remain unchanged while we are a member of the European Union.

"We are currently considering the various options as to how EU migration might work once we have left, it would be wrong to set out further positions at this stage."

Former Commons clerk Lord Lisvane suggested the Government would face defeats in the House of Lords but insisted the upper chamber was unlikely to block the Bill.

The constitutional expert, a crossbench peer, told BBC Radio Wales: "I don't think that there is any chance that the Lords will delay the Bill - if the elected House has decided not to do so then the unelected House I think could not, would not and should not do so."

The Lords could ask the Commons to "think again" on the position of EU nationals resident in the UK and the terms of a final parliamentary vote on the deal, he acknowledged, but they were likely to give way rather than engage in a lengthy parliamentary battle on the issues if MPs rejected the changes.

"I think the Lords will be extremely ill-advised to do anything else and I don't think there's any chance that they would," he said.

Liberal Democrat leader Tim Farron rejected Ms Truss's assertion that Article 50 was irrevocable and added: "This Government is trying to do everything it can to deny the public a vote on the Brexit deal.

"The Liberal Democrats will fight to give the people the final say so they have a chance to reject a disastrous hard Brexit instead of having it imposed on them."