I think you're a bit obsessed with whether it's a good cause or not, when the better question is, "is it an appropriate response or not".
The law of the land also covers criminal damage, crimes of or threats of violence, and conspiracy to commit the above, quite well. What does making Palestinian Action a terrorist group add to that - at least whilst they claim to be non-violent?
As for the politics of it, we seem to have a Labour government that is now cracking down overtly on pro-Palestinian protest, whilst doing the square root of fuck all about the Israeli state literally committing genocide and ethnic cleansing in Gaza (actual violent terror).
Personally, I don't think this approach is a vote winner for them.