Family of the detained couple said a recent meeting with UK Foreign Secretary Yvette Cooper “produced little more than a commitment to wait for more information before deciding on next steps”.
Mr Bennett said this was “deeply concerning”.
He said: “The British are waiting for a sentence before acting, the Iranians are deciding what sentence to hand down.
“And in the middle of this diplomatic stalemate are my parents, innocent people caught between two systems moving too slowly.”
The Foreign, Commonwealth and Development Office said officials “continue to raise this case directly with the Iranian authorities” and were providing consular assistance to the couple.
The government advises against all travel to Iran because of a “significant risk” of arrest and says connections to the UK “can be reason enough for the Iranian authorities to detain you”.
