What do you say to the rozzers when you get stopped for something petty?

i'm amazed at their pettyness and put up an argument, which resulted in me having a full background check, a full search, including my bag and even my shopping, and a £30 fine.

What reason did they give for the search? They're only allowed to perform a search if they have reason to believe you're carrying something to commit the crime they're accusing you of (i.e. not justified for cycling on the pavement), or if there was a crime in the vicinity that you were being searched in relation to. By law, they're required to tell you why this is necessary.

Otherwise it's just an abuse of powers.

I suspect the latter...