Yvette Cooper is facing a Labour backlash at plans to ban Palestine Action in the wake of RAF planes being vandalised.
The Home Secretary is due to update MPs later on proposals to make it a criminal offence to belong to or support the group.
But Labour politicians have criticised the step as too far - while police have voiced concerns about a protest against the move due in Westminster later.
Ms Cooper is acting after Palestine Action posted footage online showing two people inside the base at RAF Brize Norton in Oxfordshire.
The clip shows one person riding an electric scooter up to an Airbus Voyager air-to-air refuelling tanker and appearing to spray paint into its jet engine.
