If you are flying in Europe or UK Dom you can do this on BA.com.
Start by requesting "economy (lowest)" - then on agree to upgrade one or two sectors to semi-flexible (i.e. charge £30 to change).
The upgraded sector (s) will be in B or H the others will be in K, M, R, V or N.
This doesn't work on longhaul as all fare classes apart from N are semi-flexible so you can't guarantee getting a B or H fare.