Among those backing the demand by campaign group Wales for Europe for a vote on any withdrawal deal are two shadow ministerial aides.
Anna McMorrin and Tonia Antoniazzi are parliamentary private secretaries to shadow cabinet members.
The Tories have called on Mr Corbyn to sack them from their posts after the referendum call.
Mr Corbyn has repeatedly said Labour does not support a second national poll and fired Owen Smith as shadow Northern Ireland secretary for proposing one.
The MPs, along with Welsh Assembly members and councillors, signed an open letter from Wales for Europe, which stated: “The issue now is what we think about the Brexit deal that the Prime Minister brings back.
“Will it be the right deal for the people of Wales and the rest of the UK? Will it secure a good future for our young people and allow them to thrive? Will it help protect and grow the number of well-paid, highly-skilled jobs that Wales needs?
“One thing we already know is that many of the promises made during the referendum campaign are not going to be kept.
“We know there are a whole raft of issues that were never, or hardly ever, discussed in the referendum, which are now extremely important.
“The Irish border is one and that is one that matters for Wales because our ports could suddenly find themselves as part of a hard-economic border with Ireland. There are many others.
“For all these reasons we are coming together, on a cross-party basis, to speak out for the people of Wales and to demand, for them, and for everybody else in the UK, a people’s vote on the final Brexit deal.”
Tory MP Suella Braverman said: “If Labour really respects the decision the people took in the referendum, they must remove Anna McMorrin and Tonia Antoniazzi from their positions.
“Labour’s behaviour has shown a determination to frustrate Brexit and a failure to act now would confirm they have no interest in working to make a success of it.”