Only 33 MPs backed calls for a second referendum, with the amendment roundly defeated with 340 opposed to it.
It came ahead of the final Commons vote on the Brexit bill and whether to send it to the House of Lords for the third reading.
The amendment, spearheaded by Lib Dem leader Tim Farron, was resoundingly rejected in the house.
The MP had put forward the additional clause to the European Union (Notification Of Withdrawal) Bill, which if passed would have required Prime Minister Theresa May to outline the process to ratify the UK’s new relationship with the EU.
Currently in the third day of debates on the Brexit Bill, Mr Farron had previously said he wanted to prevent the UK from going “over the cliff” if the Government was unable to negotiate a good deal once Article 50 is triggered.
Mr Farron said: “Tonight, the Labour leadership wrote a blank cheque to the Conservative government.
“The Conservatives are not enacting the will of the people, they are twisting the referendum result and choosing a hard and divisive Brexit outside the single market – an option that was never on the ballot paper last June.
“Labour tonight have lost the right to be called the official opposition. History will judge them harshly for their failure to stand firm in defence of future generations of Britons who will suffer as a result.
“This was the very moment that the country needed a bold and competent opposition. It also needed Conservative MPs who would put their country before their party. It didn’t get either.
“Britain needs a progressive party that is serious about power and positive about Europe. Liberal Democrats are ready to take up the mantle.”
The 33 rebels came from Labour, the Lib Dems, the SDLP, Plaid Cymru and the Greens.
The Labour MPs are Heidi Alexander, member for Lewisham East, Ben Bradshaw, member per Exeter, Ann Clwyd, member for Cynon Valley, Ann Coffey, member for Stockport, Neil Coyle, member for Bermondsey and Old Southwark, Geraint Davies, co-op member for Swansea West, Helen Hayes, member for Dulwich and West Norwood, Dr Rupa Huq, member for Ealing Central and Acton, David Lammy, member for Tottenham.
Also from the Labour benches voting for the amendment was Fiona MacTaggart, member for Slough, Rachael Maskell, co-op member for York Central, Ian Murray, member for Edinburgh South, Andy Slaughter, member for Hammersmith, Owen Smith, member for Pontypridd, Jo Stevens, member for Cardiff Central, Stephen Trimms, member for East Ham, Catherine West, member for Hornsey and Wood Green, and Daniel Zeichner, member for Cambridge.
From Mr Farron’s own party, including himself former leader Nick Clegg, member for Sheffield Hallam voted in favour, as did Norman Lamb, member for North Norfolk, Greg Mulholland, member for Leeds North West, Sarah Olney, member for Richmond Park, John Pugh, member for Southport, and Mark Williams, member for Ceredigion.
The remaining MPs are Mark Durkan, member for Foyle and Alasdair McDonnell, member for Belfast South, Margaret Ritchie, member for South Down, all from the Social Democratic and Labour Party.
From Plaid Cymru Jonathan Edwards, member for Carmarthen East and Dinefwr, Liz Saville Roberts, member for Dwyfor Meirionnydd, and Hywel Williams, member for Arfon all voted in favour.
And lastly from the Greens former leader Caroline Lucas also voted for the amendment.