The government’s Brexit bill has passed through Parliament after Theresa May saw off a revolt by Tory MPs.

Peers accepted the amendment to the EU (Withdrawal) Bill sent to them from the House of Commons, meaning the bill now goes for Royal Assent, becoming law.

Earlier, the government won the vote 319 to 303, after assurances were accepted by would-be rebels that MPs would have a meaningful say, reports BBC.

The PM called it a “crucial step” in delivering a “smooth” Brexit.

May said: “Today’s votes show people in the UK, and to the EU, that the elected representatives in this country are getting on with the job, and delivering on the will of the British people.

“Over the next few weeks we will publish more details of our proposed future relationship with the EU in a White Paper, and will bring the Trade and Customs Bills back to the House of Commons.

“But today has been an important step in delivering the Brexit people voted for, a Brexit that gives Britain a brighter future, a Britain in control of its money, laws, and borders.”

Before the Commons vote, Dominic Grieve, leader of the would-be rebels – who wanted to ensure MPs had the power to stop the UK leaving without a deal – said the “sovereignty of Parliament” had been acknowledged.

Both sides have claimed victory with Stephen Hammond, a pro-EU MP who eventually sided with the government, suggesting ministers had agreed to give Parliament a “real say” on top of other concessions.

But international trade secretary Liam Fox said nothing had really changed and the option of a no-deal Brexit had been left firmly on the table.

“There is no change to the fundamental issue here, which is the government cannot be forced by Parliament to negotiate something which it does not want to do,” he told the BBC.

He said the government had “to be able to hold out in our negotiations the prospect of no deal” otherwise the EU would get the upper hand.

On Wednesday evening, following the Commons vote, Leader of the Lords Baroness Evans of Bowes Park said the EU (Withdrawal) Bill had been “debated at length” and was very different as a result of amendments tabled by the Lords.

“I believe our role now is to accept their view as expressed in a vote a few hours ago,” she said.

Peers approved the government’s proposal without a vote.

The UK is due to leave the European Union on March 29, 2019 and negotiations have been taking place over the terms of its departure.