Harman, a former cabinet minister who was acting leader in 2015, added: “Can we have statement from NEC on this? Policy is AWS when replacing woman MP 50% AWS in others till we achieve parity. Has policy changed?”
One female Labour MP told HuffPost: “We need to keep the status quo in seats where women are standing down, at the very least. But if you don’t do that, then you need to do even better among the seats where men are standing down.
“The talk is about letting members decide, but that only seems happen where it suits the leadership.”
A shadow Cabinet minister added that there would be “ructions” in the Parliamentary Labour Party (PLP) over the decision.
A spokesman for Vauxhall Labour Party told HuffPost UK: “We are extremely disappointed to learn this morning that the NEC has rejected our call for an All Women Shortlist in selection of our next MP.
“Vauxhall Members unanimously passed a motion last month making this request, and we are concerned that NEC members with no connection to the local party have taken this decision out of the hands of local members.
“We call on the NEC to formally explain their decision to the CLP, and reconsider, respecting the decision and democratic wishes of Vauxhall members.
“There is a long-standing tradition of where a retiring MP is a woman, she is replaced by a woman. By breaking with this we put at risk Labour’s efforts to ensure 50% of its parliamentary party are women.”
However, the local party called on the NEC to allow Vauxhall to begin its selection process “immediately” because of the threat of an autumn general election, adding “we will not stand for a candidate to be imposed by backdoor means on the constituency if a snap election is called”.
Many local Vauxhall members want the party to ensure the local BAME population is represented.
Two leading Corbyn allies, Momentum’s Laura Parker and political secretary Katy Clark, are seen as contenders, but the seat will be hotly contested by others too.
Senior Labour sources defended the NEC decision and one NEC source pointed out that in the nine ‘defector seats’ where MPs had quit the party for Change UK, independents or Lib Dems, six were now all-women shortlists.
It is understood that Bury South, where former MP Ivan Lewis was suspended, may be subject to an all-women list.
A spokesman said: “The Labour Party has more women MPs than all the other political parties combined and we are committed to improving diverse representation at all levels of the party.
“In the next election, women candidates will be standing in more than two thirds of our target seats.”
Some 72 women candidates have been selected in 102 target seats for the next election and the party still has the aim of a 50-50 gender balanced PLP by 2020.