Short answer: no CE or UKCA mark means a shop legally cannot sell the toy, no matter how good its condition. This isn't the shop being fussy — it's UK product safety law.
The mark is usually printed or moulded directly onto the toy itself, or on a permanently attached label — not just on packaging you're likely to have thrown away. Check the underside of plastic toys, the base of soft toys' sewn-in labels, or the battery compartment of anything electronic.
CE marking is the older EU standard; UKCA is the UK's post-Brexit equivalent. Most shops currently accept either, since a transition period has allowed both to remain valid — but always check with the specific shop, as this has been subject to change.
Check the shops currently accepting toys before you set off.