| Yes your 802.11b card will work with any wireless network/router that has that standard (and almost all do), but the transfer rate is not as high as some of the later standards.
If you are showing 576kb on your connection then you are not connecting at 2mb - that's half a mb. It's possible that you've not been upgraded by BT yet (I take it you are with BT on 512Kb unlimited download at the mo - going to 2mb with a free upgrade) | 
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