This decision follows a U-turn on welfare cuts, which has left a significant £5bn hole in Labour's spending plans.
Senior Labour figures have indicated that potential tax increases may be necessary to offset the financial implications of not approving welfare changes.
Education Secretary Bridget Phillipson stated that recent decisions have made future spending choices, particularly those aimed at tackling child poverty, more challenging.
The move is expected to cause further discontent among Labour backbenchers, while critics argue the cap contributes to child poverty.