The government has suffered four Brexit bill defeats in the House of Lords in one day.

Peers voted by 311 to 233 to remove the government’s fixed European Union ‘exit day’ from the legislation, following an earlier vote to allow the UK to participate in EU agencies.

Later in the evening, despite an abstention by Labour frontbenchers, an amendment seeking continued UK participation in the European Economic Area (EEA) was carried by 245 votes to 218.

Labour had whipped its peers to vote against the amendment, as remaining part of the single market is not the party’s official policy – but 83 defied their leadership.

Lib Dem Lords leader Dick Newby said the victory sent a “clear message to those sat round the cabinet table”.

“Parliament won’t just sit back while Theresa May leads us towards a hard Brexit,” he added.

“245 peers from all parties and none have voted to stay in the single market and protect the UK economy, defeating a government hell-bent on pursuing ideology over prosperity.”

The government previously passed amendments during the bills committee stage to define exit day as “11pm on 29 March 2019”.

Critics warned it would undermine any transitional period, making it illegal for the UK to extend Article 50 negotiations – even if the EU27 unanimously agreed to do so and denying UK ministers flexibility in the negotiations.

According to Lords insiders, the second cross-party amendment to succeed on Tuesday sought to “reinstate the provisions that were in the original version of the bill; and to make it clear that regulations appointing exit day require the formal approval of both Houses of Parliament”.

Newby, who was one of four peers who tabled the amendment, said: “It was frankly ridiculous to enshrine this date in law from the get-go.

“In negotiations you have to be flexible and willing to change direction if it is not in your best interests, and putting this date down as a bench-mark was never in the best interests of the UK.”

Baroness Angela Smith, Labour’s leader in the upper house, said the votes had afforded MPs a chance to consider the “finer details” of the Brexit bill.

“On our future working relations with EU agencies, many people – including within government – are only now becoming aware of the massive issues raised by our departure that ministers need to get right,” she added.

“It was also a nonsense for the government to include a fixed exit date – something that could overshadow the crossing of every ‘t’ and dotting of every ‘i’ in the negotiations.”

Baroness Smith said the amendments were not seeking to stop Brexit, but address the “fine print of when and how the agreements are concluded”.

Labour MP Chuka Umunna, who had lobbied for peers to support all three amendments through his role with pro-Europe campaign group Open Britain,  said: “This is a stunning victory for those who want to protect jobs and trade and keep our businesses linked to our biggest market.

“And it also marks a decisive vote in favour of protecting the Good Friday Agreement and the Irish peace process.”

The bill will now go back to the Commons for MPs to have a final say.

“I hope that the Labour front bench will support UK membership of the single market through the EEA, which is what the overwhelming majority of our members and voters want,” Umunna added.

“We simply cannot aid and abet this hard, destructive Brexit.”

Peers also voted in favour of a later amendment to give Lords the power to refer statutory instruments back to the Commons.