Lord Mandelson says the public will change its mind about Brexit when it sees the dismal likely outcome to the negotiations – including no fall in immigration.

The former Labour Cabinet minister also predicted the House of Lords will force changes to the Article 50 Bill this week, on the key issues of the rights of EU citizens and a ‘meaningful vote’ on the final deal.

And he urged fellow peers to press the Commons hard to accept those changes saying: “I hope the House of Lords will not throw in the towel early.”

On whether the public could yet swing against Brexit, Lord Mandelson said people would realise they were being offered less trade, at a high cost – and no real cut in immigration.

“Is that a reasonable deal? Don’t you think the public will have something to say about that outcome when the negotiations end? I think they will,” he told the BBC’s Andrew Marr programme.

Many people were having “collywobbles” about the prospects for Brexit, he insisted – despite polls suggesting voters have not changed their minds since last June.

But Elizabeth Truss, the Justice Secretary, dismissed Lord Mandelson as a “blast from the past” who was “trying to frustrate the will of the people”.

Theresa May has made cutting immigration her ‘red line’ in the Brexit talks, by ending freedom of movement of EU citizens – raising expectations that numbers will fall.

But Lord Mandelson said: “We're going to see less trade, you're going to see Britain paying through the nose for the access that we want to negotiate.

“But you're also going to see, broadly speaking I suspect, the same number of migrants coming to this country as now - partly because already half of the migrants don't come from the EU, they come from the rest of the world, and, in the case of those who come from Europe, we need them to fill jobs in our economy.”

The European Union (Notification of Withdrawal) Bill reaches the Lords tomorrow, when up to 150 peers are expected to try to speak in an initial two-day debate.

Lord Mandelson said he was confident an amendment will be passed to give 3m EU citizens in the UK an immediate, unilateral guarantee that their rights will be protected after Brexit.

He also forecast success for an attempt to ensure Parliament is given a decisive vote on any final deal that the Prime Minister secures – and, crucially, if she fails to agree one.

In the Commons, Keir Starmer, Labour’s Brexit spokesman, claimed victory when ministers conceded a vote before the European Parliament starts its consideration, probably in late 2018.

But the assurance was verbal only – and could leave Parliament with an unwanted ‘take-it-or-leave-it’ choice, which would see Britain crash out of the EU with no deal if Ms May’s is rejected.

Lord Mandelson said peers wanted to “reinstate” a proper meaningful vote at the end of the negotiations kick-started by the triggering of Article 50.

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.

Asked 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.