This should clear things up:

https://www.britishairways.com/en-us...age-allowances

In short, business (whether CW or CE) is 2 x 32 checked baggage, unless Emerald in which case a third bag (also 32kg) would be permitted.

As a side note, oneworld Sapphire is permitted 2 x 32 checked baggage regardless of cabin, except for hand baggage only fares, which don’t permit any checked baggage regardless of status.

As far as I know, hand baggage only fares are still only in Economy on British Airways, though apparently there are carriers applying such selling strategies to Business Class, so in time that may change.