Just sharing my experience of literally just now.

Late booking meant I got allocated to a middle seat in WT+ which causes minor inconvenience due to some health things (basically I need to use the facilities more regularly than most). Phoned last week and was told sorry but the bassinets have not yet been released. At approx T-72 looked on MMB and saw that they were "available" but then selecting them got a message saying I couldn't because I didn't have an infant.

Tried again just now, same result, found this post on FT mentioning that I had to call. Called BAEC just now and they moved me straight into it.