The message comes in the wake of the London bombings and the shooting by police of Brazilian electrician Jean Charles de Menezes.
It emerged after the shooting that Metropolitan Police guidelines allow officers to shoot a suspect in the head if they believe he is a suicide bomber. This is to avoid setting off any explosives that might be attached to the suspect's body.
Matt O'Connor, founder of Fathers 4 Justice, said: "We have been told by the Metropolitan Police that if we try to repeat any of last year's stunts, our members could end up getting shot.
"We were told at the time that when former member Jason Hatch scaled Buckingham Palace last September, he was minutes away from getting shot. But the police said if he did that now, he would be shot on sight."
A spokesman for the Metropolitan Police did not deny the claim. He said: "We always advise organisations to remain within the law, especially during this time of heightened sensitivity. We would advise groups to avoid acting recklessly at sites of significance."
O'Connor believes the policy will affect other groups too. He said: "We have always sailed pretty close to the wind, but this is going to make it even harder.
"This will inevitably impact on other organisations engaged in non-violent campaigning. The new police powers are effectively eroding the very freedoms they are meant to protect."
- See News Analysis, page 10.