No problem - Happy to Help
The floating floor thing is probably not needed. The main reason I was suggesting it is that you have train tracks nearby and I know from having lived in London, the LF vibration can carry over very long distances and for dynamic recordings, the only way to get around this is by floating the floor.
Rann Trivia Fact #258. David Grey's Album - White Ladder, was made for under £5k and completely recorded With Lestyn Polson in David's Camden High Street Flat (my old hood). If you listen carefully, at very quiet points on some tracks you can hear bus/train noises rumbling in the background.
Unless this is a massive problem (which I doubt as you're only recording Vox and as said before, you can solve 90% of problems associated with that by building a simple vocal booth etc) then the floating floor is total overkill, and if not done right, can actually cause more problems with resonance etc.
TBH, just put good underlay and nice carpet down. Most people thing wood floors in studios and it looks better but Carpet is a no brainer for studios. Anything nice and thick.
However, when it comes to the walls, get it right. Quiertrock is available in the UK although it's expensive. I've worked with both real quietrock, and ghetto quietrock (two layers of normal drywall with green glue between) and tbh, the results were virtually negligible difference. Even though they won't tell you this, Greenglue takes several months to really work but it's not like it's going to be a temp installation for you.
I will saying just going with straight up QR is easier, where as GQR may work out slightly cheaper for materials but it is more labor and time consuming, so you have to find our where your sweet spot is in terms of value. If labour and time is real cheap, then go GQR, if not, the QR.
Which ever design (and I haven't even got in to installation mathods yet such as RC clips etc) you HAVE to make sure the walls don't touch the floor or cieling or each other. You'll need a 1/4" gap between each surface, and you'll need people who can work accurately as normal acceptable builder's tolerances are as high as 3/4' off in any direction and still classed as OK. Just make sure you stipulate thhis clearly to the drywall/plasterer's before and make then sign it. Then, before any wet plasterwork is done (i.e. after the drywall has been affixed), just go around and double check it all has a gap of 1/4" between each surface.
You're then going to use acoustic sealant in those gap, and let is set before they do any wet work. It's actually a lot easier than it sounds. Bear in mind though QR is quite tough stuff - you can't just use a plaster knife or box cutter like you can with normal drywall. You'll need a reciprocating saw or a circular bed saw to cut/
Now on to hanging the drywall.
The RC clip method is best shown in this video:
It looks more complicated than it actually is, and the video also explains the gaps between each surface. The clips and resiliant channel are fairly cheap, so as mentioned, the money with this method is in the labor. You can certainly do this all yourself, but I would get a drywaller/plasterer in to manage and finish the project.
As for the type of drywall, if you're going with the RC method, you probably don't need to use QR, as the decoupling effect combined with the resonance air gap trap will be enough for your needs.
Now if you decide not to go the RC route, then you could just get away with using green glue to sandwich two layers of 5/8ths normal drywall together, then attaching that to the breeze blocks with green glue and anchor screws.
One caviat doing it this way; you cannot have an airgap with this method so you won't get as much low resonance absorbtion benefit as the RC method. The reason you can't have a airgap is the triple leaf effect. Anytime you have 3 (or a multiple of three) layers, it can have the opposite effect in that it actually creates a resonance chamber as the layers reverberate with each other.
The two layers of drywall are necessary though, so that sound hits the first one, gets dissipated by the green glue decoupling to the next sheet - essentially the sound energy gets transfered in to heat due to it being transferred in to kinetic energy as the compression and rarefaction turns in to physical movement along the surface of the drywall. You then want to decouple this sandwich from the wall as much as possible by using green glue and screws dipped in acoustic sealant.
Again, the big thing with this one is to make there are no places of airgaps along the breeze block wall, and you need a little bit of a smotth surface for the glue to bind to so you'd need to do a quick plaster skim on this.
RC clips will offer the best result but it's dependent on more labor so it might not be cost effective, and GG sandwich will work out cheaper.
You can do the same for the ceiling (either method) or do a drop acoustic ceiling and plenty of strategically placed some sound batt in there.
Let me know if you need any more help!