It's not normally police who issue the penalty notice, but local council staff. This means there's a lot of variation across the country. Some councils outsource this to companies who are a bit too vigorous in giving penalty notices. The aim is to prevent litter, not to raise revenue, so they're supposed to give you a chance to pick up your litter to avoid the fine but some don't do that.
https://www.gov.uk/guidance/fixed-penalty-notices-issuing-an...
The advice about when to, and when not to, issue FPNs covers the point about giving people the opportunity to pick up litter: https://www.gov.uk/guidance/enforcement-officers-issuing-fix...
That seems like an ineffective mechanism. Just litter and pick it up in the very rare cases where you get called out.
If I were council dictator for a day, I would make the fines stiff and immediate but require that 100%^1 of the revenues are refunded to all residents at the end of each year.
That way there's still a stiff disincentive to littering, but no significant incentive for abusive/dishonest enforcement.
[^1]: (perhaps sans some low and more importantly fixed amount to cover enforcement costs)
Makes friday drinks (and being stupid and inconsiderate) way more expensive (it was £85).
I always thought cigarette butts were something that are harmless and break down easily.