Just watching Street Crime UK, and noticed an officer threaten to
arrest a guy for swearing. Fair enough. The lad then refuses to
identify himself, and is arrested. However, the officer simply says

snip

Incidentally, the chap refused a fixed penalty, and opted for his day
in court instead.

Often a good gamble as there's a chance the magistrates will find you
not guilty in spite of the good evidence , or that the police and cps
cock things up

Sounds like he was arrested for not giving a name and address (because
he hadn't sworn after the warning). As I understand it that isn't a
crime but an arrest may be made in order to determine name and address.

Even if he was swearing then someone needs to be found who was "likely
to be caused harassment, alarm or distress" (and, at least in my view,
police constables have little credibility if they pretend to be alarmed
that people swear).

So I can't see what the fixed penalty was for unless something is
missing from this account.