Theresa May will be forced to order MPs to throw out an immediate guarantee that 3 million EU nationals can stay in Britain, after a humiliating defeat in the House of Lords.

Peers defied the Prime Minister by voting by 358 to 256 – a majority of 102 – to insert a clause in the Article 50 Bill to ensure EU citizens will have the same full rights to live and work here after Brexit.

The vote will infuriate Ms May, who had urged the Lords not to amend the Bill – even sitting on the steps of the royal throne herself last week, to pile on the pressure.

It means she will have to attempt to overturn the defeat in the Commons next week, when Tory MPs will be under pressure to stage their own revolt.

And it suggests Article 50 cannot be triggered for another two weeks, although the Prime Minister will still meet her deadline of the end of the month.

The Government described the result as "disappointing" but signalled it intended to reverse the result when the Bill returns to the Commons.

The defeat came after the Lords refused to be swayed by a last-gasp letter sent by Home Secretary Amber Rudd, believing it failed to give any new meaningful assurances.

Instead, peers of all parties lined up to criticise the Ms May’s stance – some accusing her of using EU citizens as “bargaining chips” in the looming Brexit negotiations.

Viscount Hailsham, a Conservative, said: “This House can in fact make a unilateral decision and indeed a unilateral guarantee and that is what we should do.

“Let us all remember how shocked we were when Idi Amin expelled the Asians from Uganda, so shocked that we offered them refuge in this country.”

The former head of the civil service and independent crossbencher Lord Kerslake said the 3 million EU citizens had come to the UK in “good faith” and contributed enormously to the country.

The issue may not be resolved quickly, which created “risks for a desperately needed skilled staff with devastating consequences” for home building and the NHS.

Lord Campbell of Pittenweem, the former Liberal Democrat leader, warned it would be “catastrophic” for public services and the economy to lose EU workers.

And Baroness Hayter of Kentish Town, Labour’s Shadow Brexit minister, said: “These people need to know now – not in two years' time or even 12 months' time. They simply can't put their lives on hold.”

But the Archbishop of York, the Most Rev John Sentamu, said the short Bill should be left as it was, or it would become a “Christmas tree” with all sorts of “baubles” added to it.

And Lord Tebbit sparked anger when he accused peers attempting to protect the rights of EU nationals of “thinking of nothing but the rights of foreigners”.

To gasps and jeers, the former Conservative Cabinet minister asked: “Why is everybody here today so excited about an amendment which looks after foreigners and not the British.”

The Opposition parties will hope to tempt more Conservative MPs to rebel when the amendment goes back to the Commons – but just three did on the controversy last month.

On that occasion, the Government blocked a bid to protect EU nationals’ rights with a majority of 42 – suggesting around 25 rebels will be needed.

The Prime Minister has said the issue is a top priority, but will not act until she receives “the same reassurance for UK citizens living in the EU”.

The Polish Social and Cultural Association described the Prime Minister’s stance as “immoral”, warning nationals are too scared to report hate crimes because of confusion about whether they will be able to remain.