The police aren’t so much stretching things as going beyond oversplits and into full contortionist territory here.
When the Hate Crime legislation was being debated the House of Lords discussed the fact that wearing swastikas &/or “singing certain songs” could be used to evidence a crime was a Hate Crime. These indications are in the relevant CPS guidelines. That’s it for swastikas in English & Welsh Law.
It honestly sounds as if they’re trying to go for a public order offence - as I said, contortionism. Especially if you consider, with reference to the swastika, the HAD of Unexpected Reenactment Nazis parading through your town for funsies.