When I was on a survival course at Boscome Down and they spoke of a light aircraft going down in the Solent over twenty years ago.He got his mayday out SAR and coast guards (knew the he was in the Solent) were called out and yet it took almost an hour to find him (almost dead).
They used it as an example of how likely it would be that you get found if you went down in the North Sea (or worse)!