Some, not all, unknown amount, the 5870 came out while previously you could get 285gtx's for £250ish, maybe less, after the 5870 came out it went up to £350. Largely because Nvidia had very little stock left and they wanted there to appear to be stock for as long as possible so raising prices put most people off actually buying them.
In that situation Nvidia hoped to have 480gtx's on sale so stopped production on the 285gtx long before and got screwed, that is less likely to happen this time but then making 580gtx's to sell at £180-200 is also going to be pretty uneconomical............ it could go either way, crash in all Nvidia prices, or stopping most production and silly prices, or everything but the 580gtx crashing.
Personally I think you'll be looking at 560ti 2gb's at £150ish, and 570gtx under £200 at some point in January while the 580gtx gets a cut but not a huge amount.