A Labour whip and an aide to deputy Labour leader Tom Watson quit in order to vote against a second Brexit referendum as the party’s divisions on the issue were laid bare.

Stephanie Peacock resigned from the whips office, saying she wanted to “respect the result of the 2016 vote” and her constituents in Barnsley East would expect her to “honour that promise”.

Ruth Smeeth resigned as parliamentary private secretary to Mr Watson, saying she had a duty to “support the will of my constituents” in Leave-supporting Stoke-on-Trent North.

Two other frontbenchers also rebelled to oppose a second referendum, even though Labour’s official policy is to keep the option on the table.

The party’s MPs had been told to abstain, but a total of 24 backed the call to delay Brexit in order to hold a second referendum, with 17 opposing it.

Shadow communities minister Yvonne Fovargue and shadow health minister Justin Madders also voted against the second referendum amendment in the Commons.

Labour leader Jeremy Corbyn’s office said it was a matter for the whips to decide what action, if any, they would face.

The amendment, pushed by The Independent Group’s Sarah Wollaston, was overwhelmingly defeated by 334 votes to 85 as the bulk of the Labour Party stayed away from the voting lobbies.

In her resignation letter, Ms Peacock told Mr Corbyn: “I was elected on the Labour manifesto that pledged to respect the result of the 2016 EU referendum. The people of Barnsley elected me to honour that promise and that is what I did tonight.

“I felt in all good conscience I had to vote tonight to clearly rule out any form of second referendum.

“I believe the people spoke in 2016 and we need to enact their decision.”

Ms Smeeth said: “This was a difficult decision but I have a duty to support the will of my constituents. We need to leave, and leave with a deal that works for the Potteries.”

Meanwhile, the Labour hierarchy – Mr Corbyn, shadow chancellor John McDonnell, chief whip Nick Smith and shadow Brexit secretary Sir Keir Starmer – held talks with two backbenchers who have put forward a plan to back Theresa May’s Brexit deal in exchange for a referendum.

A Labour Party spokesman said they had a “useful and constructive discussion” with Peter Kyle and Phil Wilson “as part of Labour’s engagement with MPs across Parliament to find a practical solution to break the Brexit deadlock”.

In the Commons, Mr Corbyn said: “I reiterate my conviction that a deal can be agreed based on our alternative plan that can command support across the House.

“I also reiterate our support for a People’s Vote – not as a political point-scoring exercise but as a realistic option to break the deadlock.”

The 24 Labour MPs who voted for the second referendum amendment were: Tonia Antoniazzi (Gower), Ann Clwyd (Cynon Valley), Neil Coyle (Bermondsey and Old Southwark), Stella Creasy (Walthamstow), Janet Daby (Lewisham East), Geraint Davies (Swansea West), Rosie Duffield (Canterbury), Paul Farrelly (Newcastle-under-Lyme), John Grogan (Keighley), Meg Hillier (Hackney South and Shoreditch), Ged Killen (Rutherglen and Hamilton West), David Lammy (Tottenham), Siobhain McDonagh (Mitcham and Morden), Anna McMorrin (Cardiff North), Ian Murray (Edinburgh South), Albert Owen (Ynys Mon), Tulip Siddiq (Hampstead and Kilburn), Owen Smith (Pontypridd), Alex Sobel (Leeds North West), Jo Stevens (Cardiff Central), Gareth Thomas (Harrow West), Catherine West (Hornsey and Wood Green), Martin Whitfield (East Lothian), Daniel Zeichner (Cambridge).

The 17 Labour MPs who voted against were: Kevin Barron (Rother Valley), Ronnie Campbell (Blyth Valley), Rosie Cooper (West Lancashire), Caroline Flint (Don Valley), Yvonne Fovargue (Makerfield), Kate Hoey (Vauxhall), Helen Jones (Warrington North), Kevan Jones (North Durham), Emma Lewell-Buck (South Shields), Justin Madders (Ellesmere Port and Neston), John Mann (Bassetlaw), Stephanie Peacock (Barnsley East), Ruth Smeeth (Stoke-on-Trent North), Gareth Snell (Stoke-on-Trent Central), John Spellar (Warley), Graham Stringer (Blackley and Broughton), Derek Twigg (Halton).

Lloyd Russell-Moyle (Brighton, Kemptown) voted both aye and no, which is regarded as a formal abstention.