The group, made up of MPs who quit Labour and Tory benches, has said the opposition should show a more united front over a new EU withdrawal poll.
In an open letter, TIG has called on members of the shadow cabinet to drop the “terms and conditions” it says Labour has attached to backing a bid for a new referendum.
Accusing Labour of “ambiguity” on the issue, TIG has asked if the shadow cabinet will support a cross-party Commons amendment calling for a new Brexit poll.
TIG’s spokesman Chuka Umunna said Labour needs to clarify its stance.
He said: “With just 26 days to go to the scheduled date of departure, it is absolutely vital that we all work together in the national interest to give people the final say on Brexit.
“All terms and conditions attached to a people’s vote need to be dropped and an unequivocal commitment given now to make it happen. There is no time to waste.”
The Independent Group has already tabled an amendment seeking to pave the way for a second Brexit referendum.
It came after Labour announced the party would back attempts in the Commons for a fresh public vote, if it failed to force MPs to adopt its own Brexit plans.
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