Stephen wrote

I bought an unbranded wall-wart to usb output charger
from CPC, hoping to use it to charge my mobile phone
or tablet (both are Samsung). When I connect either device
using the original Samsung cable, neither device charges.

Why is this not working?

Most likely it's a useless charger.

I read a post here some months ago saying that the PSU
and the device communicate (presumably over the data
wires) and presumably the phone tells the charger what
current it will accept?

Yes. But that communication is pretty primitive,
normally the signalling is done with static voltage
levels until you get to USB C which you arent using.

Could it be that the charger I have is not that
sophisticated and is not talking to the phone

Or not signalling what the phone and tablet expect.

or does Samsung employ some way of checking
whether the supply is a Samsung charger - I'm
not an Apple man but I think Apple do the same?

Apple actually check the cable, not the charger,
and quite a few non apple cables do work fine.

Would it work if I bought one of the charge only cables with red plugs?

Likely that is what that charger does already, doesn't
have the data wires and so the phone and tablet
doesn't ever start charging because it can't see what
it expects to see with the voltages on the data lines.

Presumably they block the signaling on the data wires?

Yes, but that is likely to be the problem that
stops the phone and tablet from charging.

Or would it be cheaper to just buy a Samsung charger?

Wouldn't be cheaper but will certainly work.

I thought the idea behind using usb charging was
that any charger could be sued for any device?

That was certainly the intentions, but things got quite
messy later when chargers started to be able to deliver
more than the original 0.5A that USB originally supported
and there needed to be a way to signal which could do
that and Apple did that differently to the others.
https://en.wikipedia.org/wiki/USB#Power