Re: Protests and petitions
Petitions certainly can have an impact, not sure about protests.
Many petitions presented have been acted upon, but they usually need 100,000 signatories for it to be brought before Parliament to debate the issue.
Anything to do with Parliamentary business is probably something that can be voted down, but with such things as e.g. animal welfare, results have been achieved, despite the whole thing being a long process.
They have to wait until there is space to debate, and then maybe a second debate. These things take months.
Here's a list of all the bills waiting to be addressed. It's very interesting.
https://services.parliament.uk/bills/