In a letter published in The Times, chief executive Mark Bogard (pictured) noted that the tax had now become too big a burden which people were avoiding rather than face paying when they move.
He highlighted that with falling receipts and a stagnant housing market it was necessary to address the situation now.
“While Brexit is being blamed for uncertainty, we have held the belief firmly for some time that stamp duty is really the glue that is gumming things up,” he wrote.
“Stamp duty is the easiest tax to avoid. Don’t move.
“Stamp duty relief for first-time buyers is helping many onto the first rung of the ladder, but there is stagnation further up.
“We call for appropriate stamp duty relief for downsizers, who end up occupying family homes when the family has long moved out.
“Also for people moving for work, rather than have them gumming up the transport system commuting for hours.”
Bogard added that doing this would help to free-up the housing market, get people moving and “give the economy a real shot in the arm.”