Yes, that's right, in UK carrying in public any object that can be or is used as a weapon (including defensively) is considered a crime. This is normally applied to knives, but if the letter of the law was to be adhered to someone who did defend themselves against an attack with a small pumpkin could be arrested for the possession of the said pumpkin... This is the madness of UK law.
I remember few years ago a situation where a dog attacked a small child and wouldn't let go, someone ran home, grabbed a kitchen knife, killed the dog and saved the child. When the police arrived they had to arrest the person who saved the child life because of the knife... Thankfully the person didn't end up being charged as no witness would testify that that person has indeed used a knife as a weapon.
You're not allowed to carry a hard fruit in a bag with the intention of using it as a self defence weapon. But if you go shopping and happen to have it on you when you're attacked you're allowed to use it to defend yourself. (And you don't need to wait for the attacker to land the first blow, you're allowed the first strike if you're genuinely trying to defend yourself).
EDIT: also, you seem to misunderstand the purpose of English arrests. Of course if you stab an animal to death you're going to get arrested. The arrest allows the police to question you, and it _protects your rights_ -- you get a free lawyer for that interview; they have 24 hours to charge or release you etc.
https://news.ycombinator.com/item?id=15372404
The first man mentioned in that article was convicted and sentenced to 6 years in prison on the sole charge of possession of this knife.
https://www.amazon.com/Sheffield-12113-One-Hand-Opening-Lock...
If the blade is under 3 inches (and isn't lockable) you're allowed to carry it.
If the blade is longer than 3 inches you need a valid reason to carry it.
(2)Subject to subsection (3) below, this section applies to any article which has a blade or is sharply pointed except a folding pocketknife.
(3)This section applies to a folding pocketknife if the cutting edge of its blade exceeds 3 inches.
The three inches is clarification around folded pocketknives, it's not blanket authorisation to carry knives less than that length.