Earlier quoted context omitted.
Clearly they do work because this one achieved quite a lot. It’s not nothing to have a Parliamentary debate on a subject because of a petition!
The number of UK Government and Parliament petitions that have led to an identifiable policy change is so small as to be statistically negligible — effectively a rounding error compared with the total number submitted.
If you think we're going to have government by petition then I don't know what to tell you.