Speaking to The Observer, Labour’s Ms Nandy said: "The government must be clear with the Israeli coalition government that concrete action will follow, including a ban on goods entering Britain from the illegal settlements in the West Bank.
"This is a major step, but such a blatant breach of international law must have consequences. It will take a level of courage that so far ministers have not been willing to show."
The proposal is seen as being tougher than previous calls by Labour for diplomatic efforts to halt any land expansion by Israel.
The Board President added: “At our meeting with Keir Starmer on 19 June, I told him that while the UK Jewish community is divided on annexation, there is far more unity on the Boycotts, Divestment and Sanctions movement.
‘’I would urge Sir Keir and the Labour Party not to go down this route. ‘’
Under the unity government deal, Prime Minister Benjamin Netanyahu can begin advancing annexation on July 1, which he has repeatedly pledged to do.
Palestinians and much of the international community say the move could scuttle any hopes of a viable Palestinian state.