Actually, we are not governed by the UK CAA, just another european CAA. Funny enough, there are a couple airplanes in our fleet that do not have flex MTOWs, for those we always have to use the actual MTOW, from what i remember those were not build for us and are leased in from external sources.
About AFMs, there is none on board anymore, the EFB contains a generic AFM for the 737, but not specific for the airplane in question, the AFM is not part of the normally used documentation anyway. There might be a storage space somewhere in the headquarter for all those original AFMs, but somehow i doubt it.
I guess as soon as there can be no money saved by the flex weight thing the company gonna drop it, as the administration of the whole thing costs money too.