You don't need to break the law to get arrested. But the powers-that-be can just pass a law that makes protest illegal, and then what? https://www.bbc.co.uk/news/uk-65542558 (For clarity: while Amnesty International calls the bill "draconian",[0] the UK has not made all forms of protest illegal for all people. A government could, and many have,[1] but the UK government has not. And while the Met has some pretty serious issues, there's nothing even remotely like the police-violence-against-protestors stuff you see in the US (e.g. Stop Cop City). Indeed, the police in the UK – even the Met – are usually doing their jobs properly! See https://www.bbc.co.uk/news/uk-67398933 for a slightly-less-cherrypicked example of Met officers making arrests at a protest.) In the US, many police departments use chemical weaponry – a war crime, if used in war – on unarmed civilian protestors.

If you're following the rules, if you're behaving as you would “on the regular”, it's not a protest.

Regarding climate change, of course people are impatient! We have no way to remove CO₂ from the atmosphere, so every month spent waiting is a month where things get permanently worse. It'll be hundreds of years before things start approaching the conditions of the average living person's childhood, and that's if we stop everything now, quickly enough that people will die from lack of infrastructure.

[0]: https://www.amnesty.org.uk/blogs/campaigns-blog/public-order...

[1]: https://www.amnesty.org/en/what-we-do/freedom-of-expression/...