After upgrading the iPad's OS (4.3.4) over the weekend, which produced no improvement to the situation, I can only conclude that the problem is something to do with the quality of the signal from the Linksys router that the iPad can not deal with. Why that has changed, I can not tell. Reluctantly, and at cost, I have given up with trying to solve the matter and I bought another router. Naturally I chose one on which I had tested my iPad's operation. I imagine that there are other routers, however I can vouch for a Netgear n300 which seems to function well. And now to eBay to off load the original router, perfectly good for everything other than iPad/iPlayer comparability.