He was joined at Number 10 by former detainee Anoosheh Ashoori and Richard Ratcliffe, who went on hunger strike twice in a bid to get his wife Nazanin Zaghari-Ratcliffe freed from Iran.
Mr Bennett, from Folkestone, Kent, said: “I need to know they [the government] are working as hard as they can to get them home.”
The petition was handed in after a choir of supporters sang Stand By Me.
Every day in prison “chisels away at their mental and physical health,” Mr Bennett said, adding: “They are not spies for the British state.”
He was speaking on Saturday as Iranian media reported another day of clashes between security forces and demonstrators.
Protests erupted in Iran last Sunday over inflation and currency devaluation, after the Iranian rial hit a record low against the US dollar.
At least eight people are reported to have died during the week-long protests, as of Saturday morning.
On Friday, Donald Trump warned Iran that if Tehran “violently kills peaceful protesters” the US “will come to their rescue”.
Iran’s foreign minister Abbas Araghchi said the US president’s warning was “reckless and dangerous”.
Mr Bennett described it as a “worrying situation”.