Petitions normally have a low chance of changing anything. If you look up the definition of petition it basically means beg, mainly when an inferior begs to a superior.
Protest means pro (for) and test (experiment), so if you are protesting you are for the experiment and the police will almost certainly beat the crap out of you.
If you "Object" to something that just gives a third party the chance to overrule the objection.
They key word people need to be using in situations like this is
Reject.
If you send a letter to your MP and reject something they don't have any easy outs. If millions of people send notices of rejection it will convey much more weight than any petition ever will.
Send your letters to your elected officials as a Notice of Rejection.
That way they don't have any chances to deny overrule or retaliate by force.
We are ruled by words and our words convey as much power as theirs. Don't give them any power by choosing the wrong words.