An Arab rights organisation, the Council for the Advancement of Arab British Understanding (CAABU), wants the public to petition MPs to sign a motion against the wall's construction.
Mathew Jackson, CAABU Information and Campaigns manager, said on Tuesday the wall is a violation of Palestinian rights and a threat to peace.
He said: "We hope to get about 40 MPs supporting this motion. I think it is a good issue for people to come together on because the wall is something that most people are against."
But he added: "We still don't feel it is a big enough issue in people's minds so we hope this motion will highlight the injustice of it all."
A British foreign office spokesman also condemned the wall.
He said: "The British government has been consistent in its oppostion to the wall - we feel it is an obstacle to lasting peace in the region and an impediment to the success of the peace process."
British Foreign Secretary Jack
Straw says the wall is an obstacle
And he denied the government was treating the Israelis with kid gloves.
"We have denounced the wall on several occasions in an unambiguous manner and we have made our concerns clear to the Israeli government," he said.
The apartheid wall is made up of reinforced cement, barbed wire, fences, trenches, guard towers and security roads.
It cuts deep into Palestinian land and will incorporate approximately 91% of the West Bank's illegal Jewish settlements.
When completed, it will leave 45 to 55% of the West Bank on Israel's side of the wall.
It also violates the Geneva Convention, to which Britain is a signatory, which forbids the destruction of property and confinement of people by occupiers.