Short answer: sometimes, for ordinary kitchen knives — but plenty of shops refuse all knives outright, and that's not the shop being fussy. It's illegal to sell any knife or bladed article to someone under 18, and a busy volunteer at a till isn't always set up to verify a buyer's age the way a big retailer is. Many shops decide it's simpler to say no to knives entirely than risk getting that wrong.
Most donation rules are about condition or safety of the item itself. This one is about who's allowed to buy it. Selling a bladed or sharply pointed article to someone under 18 is a criminal offence, regardless of the seller's intent, and some knives — flick knives, certain hunting or "zombie-style" knives — are restricted or banned from sale entirely under the Offensive Weapons Act 2019, on top of the age rule that applies to ordinary knives.
Large chains like British Heart Foundation and British Red Cross don't accept knives at all, as a blanket policy. Anything beyond an ordinary kitchen knife — hunting knives, multi-tools with a locking blade, anything that could be read as a weapon rather than a kitchen tool — is very unlikely to be accepted anywhere, and some of these are illegal to sell secondhand full stop.
Some shops keep secondhand knitting needles behind the counter, or won't sell them at all, citing safety concerns similar to knives. Worth knowing: the UK's Health and Safety Executive has explicitly said there's no health and safety law requiring this. It's an individual shop's own risk-management call, not a legal restriction — so it's genuinely just down to that shop's own comfort with it, not something you can appeal to a rule on.
Many police forces run knife amnesty bins for safe, no-questions-asked disposal of blades you no longer want — check your local police force's website for the nearest one. It's a better route than putting a blade loose in general waste either way.
See our wider guide on what charity shops typically can't accept, or the bric-a-brac and homeware guide for the rest of the kitchen drawer.