OK, thanks for that. It does look like at least reconfiguring the wireless router would be necessary.
In the event of either me not being able to reconfigure the wireless router (it's going to be a shared situation and not my 802.11n router so it may be problematic to start changing things too much), or in the event of the 802.11n wireless router just not being able to support 802.11b, might something like this be possible?:
I have an Apple base station ( http://en.wikipedia.org/wiki/AirPort#AirPort_Extreme...
) which I'm using at the moment fine with my 802.11b computer. Might it be possible to somehow connect my Apple base station to the already existing 802.11n wireless router somehow (by cable (ethernet?) or wirelessly)? The broadband connection in question is Sky, but I'm not sure of any further details yet, apart from it is using a wireless router.