I've never heard of a BK Elec product here in the US but haven't really looked for one; Tannoy has a better presence, but rather for speakers. Velodyne was a sub company but is now more concentrating on autonomous vehicles/lidar applications IIRC, but seems they're still around for now. There may be some subs available here from other UK speaker companies like B&W or Wharfedale, and some carry Rel. I wouldn't look to any of them in any case, altho BK Elec and XTZ for european brands seem to have some solid subs.
Here in the US we have several internet direct sub specialists like SVS, Rythmik, Power Sound Audio, Hsu Research and a few others that will get the bulk of the recommendations, and some solid DIY/AIY offerings as well. You might be able to get SVS but the others I don't think have any regular distribution there.
Your room is fairly large (and would depend on your ceiling height and if your living room is open to other rooms) and subs work off the volume of the space available to them. I have a similar sized floor area in my living room (with 2.4m ceiling height) and it's open to other rooms, so I use four fairly powerful subs (much more so than the Velodyne) to get what I want. I don't think the 8" or 10" subs you list would do a lot in your size room, even if the room is sealed off from others, and especially not if open to other rooms. Depends on how much you want, tho
I'm somewhat a bassoholic.
I prefer having the ability to set a crossover between my subs and speakers and generally use AVRs with bass management features for such; diddling only with a low pass filter to "blend" with the speakers isn't my preference. It works for some, and those who have no choice with older 2ch gear don't have a choice unless they find a sub that can provide the functionality; some subs offer speaker level connections with a high pass filter for the speakers (i.e. provide a crossover) so as not to duplicate frequencies but you need to check the sub manual carefully to see if they have such.