Does this mean that the new chisels currently on the market are better quality, therefore safer buy? I have been looking at new chisel set selling on Amazon. Some comes with oil stone and honing guide and 6x chisels in hard case set for about £25 including delivery. The steel of the new chisel set seem mostly made of CR-V alloy steel.
No - it means you'll get whatever they decide to make, which could be a good chisel for 25 pounds (or set) or it could be a lower carbon steel that is also not even hardened to its potential.
The older main line sheffield tools should be better, but there's no guarantees there either.
1% chrome vanadium drill rod (which most chisels are die forged from these days - at least anything not costing mounds of money and machined out of bar stock at a CNC boutique factory) is so cheap that there's no reason that you can't get a great set of chisels for 25 pounds from china, but the commitment to make use of inexpensive stuff and turn it into good tools is less consistent than it would've been in sheffield.
I would be surprised if brades used a middling (lower) carbon steel, but one never knows until (like in the case of the OP), they reharden the chisel. There are enough chisels on your side of the pond that if you get ten out of car boots and keep the best five, you'll likely have excellent chisels without doing anything other than dumping the low five.
So, how do you tell if older tools are substandard? You learn to reharden known spec steel and then do the same to older tools - if they come back to mediocre with proper hardening, then they're mediocre. (ohio tools and auburn irons in the US fall into this most of the time that I've rehardened them - they're not that good and Ohio tools apparently advertised making irons out of spring or strip steel - a lower cost grade).
Other failures that aren't likely would be something like having a good high carbon steel, but shorting the alloying elements (maganese, chromium or nickel or some combination) that make it hardenable. That would just be careless, but could happen.
I would say your odds of getting a 25quid chisel set and having it be usable are OK. Having them be better than undamaged or unmodified chisels from sheffield 100 or so years ago is very small. It would be possible at low cost, though, if someone actually wanted to do it in china as the per-tool cost for a die forge bench chisel is not more than about $1 manufactured in china, even with high carbon steel.