Wow! Amazing speaker design. Judging by the size, they look like they were made for an extremely large room or small hall. What is your room size/floor area? You have some very high-end gear which deserves great speakers though I can't predict the sort of sound you're currently getting (in a typical domestic sized room, I'm assuming?) from these amazing-looking speakers. Looking at the drive unit layout, I'd be surprised if they gave a decent stereo image or accurate soundstage but I would expect them to have a great sense of scale, impact and authority.
One thought strikes me: the cabinet finish of the bass box doesn't match the higher range box. And it appears to be a little wider than the higher range box too. Was this bass box added at a later date? Was there originally another bass box or did the speaker originally consist solely of the higher range box? Reason I ask is because at least one of the drivers, possibly two, in the higher range box looks to be an 8" bass driver (or at the very least, a 8" bass/midrange driver). I wonder if the higher range box is actually a full range speaker in it's own right and that the bass box was added later to provide a bit more depth/welly (to use a technical term!). If that's the case, then the 8" drivers in the higher range box may not be fed through a high pass crossover and so is fed a full range signal from the amp which means the higher range box will likely reproduce bass - at a guess, to below 100Hz - so a typical hifi active subwoofer set to reproduce frequencies below around 100 Hz should work just fine in combination with the higher range box.
I assume you have two sets of these speakers (i.e. a stereo pair)?
Clearly, if you love the sound of these speakers then it's best to consider a repair because it will be impossible for anyone to predict their sound in your listening room/space and therefore impossible to suggest similar sounding modern alternatives. Unless the 8" drivers in the higher range box are fed a full range signal, then replacing the bass box with a sub, of any kind, is hit and miss due to the unknown crossover frequency of your speakers and the inability of all quality subs that I'm aware of (though I'm not particularly familiar with the hifi/home theatre subwoofer market) to handle frequencies above about 120 - 150Hz.
This 12" KEF bass driver in the bass box is a late 1970's design called the KEF B300. A quick Google says it was used in the KEF 105.2 and CS9 speakers. I haven't checked but I'd imagine a suitable replacement would be available. Only thing is, the bass section of the existing crossover might be faulty so replacing bass drivers may not correct the problem.
I appreciate that shipping (two?) large bass boxes off to a specialist repairer is a pain and will cost a bit, but I would confidently say that the aforementioned Wilmslow Audio or Falcon Acoustics will effect a solution. No harm in giving them a call to hear what they suggest. Alternatively, there's a consumer electronics repairer in Herne Bay (
R J Electronics, Herne Bay | Tv Repairs - Yell) who may be able to help. This is not a personal recommendation of R J Electronics as I've never used them. Good luck with your quest.