About 6 months ago I planted six areca nut palms, all about 6-7 metres high, in the garden (I don't eat the nuts, but they do look pretty when they are ripe)... Yesterday strong winds snapped the top off three of them - the palm tops have disappeared completely.

I think they're dead - but is this really the case? Can they regenerate? Or do I need to replace them? Any advice would be greatly appreciated, thank you.

Generally, usually, with palms if you kill the newest emerging leaf, the plant dies, sometimes it takes many months for the other leaves to brown out. So unless you can see the spike of a new leaf coming out the top, they are probably dying. You might however wait a few weeks to see if a spike emerges.

An exception would be a clumping palm where only the branch or stalk with the damanged emerging leaf will die and the other branches or stalks will be fine.

We had an areca palm in BKK, taller than our house. All palms are subject to infection by palm weevils. After 15 years or so, the palm died and eventually the trunk came down.

I strongly suspect this is what you have going on. No solution except to cut the trees. Bummer, even if you don't chew betel!

If the crown is gone then Im 95% sure it will die , sorry.