Very bad news indeed George, and distressing for you as they were turning out to be your 'extended family'.
Magpies are notorious for predating other birds' eggs, but you say that there are a lot of projections in the plant and probably difficult for birds to get in. A likely suspect but not knowing the actual structure of the Hornbeam it's difficult to rule out another bird completely. However, I don't think they would destroy the nest. They would just take the eggs and fly away.
Cat, rat or other climbing creature? Another possibility, as they would cause damage to the nest whilst trying to get at the eggs.
You would need to do a bit of a vigil or ask around your neighbours to see if they have seen anything prowling about recently.
You thought the bird was a Thrush and you had seen one blue egg previously.
The Song Thrush nests in shady places in a bush or tree and is the usual location for the nest, which will be built by the female. The nest is cup shaped and constructed from grass, twigs, and earth. The lining is very smooth and typically comprises mud or dung mixed with saliva. The smooth, glossy bright blue eggs are spotted with black, and approximately 27 mm by 21 mm. The female incubates the eggs by herself. After the young hatch, they are fed by both parents.
Breeding starts between March and June, has between 2 to 4 clutches with 3 to 9 eggs each clutch. The incubation is between 11 to 15 days and fledging is between 12 to 16 days.
It's most unlikely that you bird will return to this bush again having suffered an attack on its nest, which is a real shame.
Laurie.