Most ex-UK I-fares (and I believe also D-fares) do not allow for upgrading with money.
Swanhunter, when did you last pay for a CW ticket yourself?
I agree that in these circumstances BA are not likely to be sympathetic. If, for example, you've been switched from the nice front cabin of a 3-class 777 to the horrid dormitory of a 4-class, that's as good a reason for wanting to switch as there is, but BA will insist "club world is club world is club world", even if you would never have bought the ticket had you known where you would end up.
HenkyBaby said something in another thread today about the fact that one of the great advantages of BA is no substitutions. Ho hum.
On the bright side, you can MFU your CW ticket, assuming it was a paid fare (or a full redemption which can in effect be rebooked) and not an MFU already. This true even though the ticket conditions say upgrades are not permitted. So look out for Z-availability - it is probably your only chance.