Stephen Beer from Christians on the Left spoke after Mr Corbyn sacked his shadow foreign secretary Hilary Benn early on Sunday morning and the shadow health secretary Heidi Alexander (pictured below) resigned.
The shadow minister for young people, Gloria de Piero, later resigned.
Shadow transport secretary Lilian Greenwood and shadow Scottish secretary Ian Murray are said to be among those on the verge of stepping down.
Hilary Benn told BBC One's Andrew Marr Show: "At this absolutely critical time for our country, following the EU referendum result, the Labour Party needs strong and effective leadership as we take decisions of huge importance for the future of our country.
"We don't currently have that and there is also no confidence that we will be able to win a general election as long as Jeremy remains leader."
In her resignation letter to Mr Corbyn, Ms Alexander said: "More than ever, our country needs an effective opposition which can hold the Government to account and which is capable of developing a credible and inspiring alternative to an increasingly right-wing and backward-looking Conservative Party.
"As much as I respect you as a man of principle, I do not believe you have the capacity to shape the answers our country is demanding and I believe that if we are to form the next Government, a change of leadership is essential."
Speaking with Premier, Stephen Beer from Christians on the Left said the situation was "fast-evolving", adding: "I would say the membership of the Labour Party, broadly speaking, is still analysing the impact of the referendum result; to be fair, many of them, having campaigned very vigorously, are probably having a weekend off at the moment.
"I think, to be honest, the answer to where the leadership of the Labour party is going and what might happen ultimately lies with the members and I don't think we've heard from them yet."
Shadow chancellor John McDonnell (pictured above with Jeremy Corbyn), seen as a possible successor to Mr Corbyn, appeared on the BBC's Sunday Politics programme where he said he would "never stand" for the role.
He said: "He was elected nine months ago, the biggest mandate of any political leader in our country, and he is not going anywhere"
"If Jeremy has to stand for another leadership election, I will chair his campaign and I think the Labour Party members will elect him again."
The Parliamentary Labour Party is on Monday expected to consider a motion of no confidence in Jeremy Corbyn which was tabled by senior backbencher Dame Margaret Hodge and seconded by Ann Coffey.