Yes, they most certainly can sting after death for some considerable time. It's not unusual for them to have this ability for many days after death.
To allow children to play around dead jellyfish is very foolish. You have to remember that the tentacles can be almost invisible under the right conditions when lying on the sand and may even be partially buried under the sand due to the intervening tides. The tentacles can be many metres long.
There are six species of jellyfish around the coast of Britain, and although the Common Jellyfish (Aurelia aurita) is generally unable to sting humans because of the thickness of the skin, another four can inject venom. These are The Lion's Mane, Compass Jellyfish, Mauve Stinger and the Blue Jellyfish. The Barrel Jellyfish can also sting under the right conditions.
The Portuguese Man o'War and the By-the-wind Sailor are also occasional visitors.
Severity of the stings is dependant upon the species, the penetrating power of the nematocyst, the thickness of exposed skin of the victim and the sensitivity of the victim to the venom.
It's best to keep the children well away.