Nematodes from Nemasys. 100% effective - best to treat in the autumn, but I believe you can still stop the larvæ pupating in the spring, which will reduce your adult population this summer.
Above all, make sure you treat this coming autumn.
As to your question - yes, flooding will kill them when you place a pot in water with the surface of the soil below the water-line (otherwise they will just crawl up to the surface) for several hours, although they will survive in any air pockets. Obviously prevention is far better than this method.

Thank you for your reply. I am a bit reluctant to use nematodes because it is interfering with the ecosystem and I wonder whether the cure could get out of hand and be worse than the problem. Regarding the ability of the bugs to survive in water - yesterday I put one bug in a pot of water and 24 hours later it looked as though it was dead, but when I removed it, a few minutes later it was moving again. Maybe they need longer immersion?

The nematodes are part of the ecosystem. They exist out there in the soil, just not in Britain. What does cause problems is the use of Neonicotinoids which damage Bees.
The length of time you would need to plunge a pot full of plant and grubs would kill the plant long before it killed the grubs. I have tried.
The adults can swim in pure bleach for 24 hours without dying, you try that and see how long you live (don't really, no definitely DON'T).
Vine weevils are a fairly recent population explosion thing mainly because of the use of their favourite medium........peat for planting.

if you suspect you have them in the pots knock the plant out wash all the soil off the roots and repot in fresh compost..
I do this regularly and then either feed the grubs [weevil larvae] to either the fish in the pond, my daughter's gerbil or they go in a dish on the bird table.

as already stated the nematodes are a natural predator and are part of the ecosystem.

Thanks Owdboggy & .Seaburngirl. I might have to invest in nematodes. Bugs that I find will go in a plate on the ground for the birds. They seems to appreciate them. Protein rich diet, I suppose.

Thanks for advise everyone. I am now finding by experiment that if I immerse infected compost in water for seven days the bugs appear to be dead - that is, no signs of life, no movement. But I may have to buy some nematodes.