Under UK Building Codes are you allowed to add an additional stopcock?
I don't why you couldn't install a new stop cock after the current one but in a more accessible location. We've installed shut off valves at various points so we can work on each sink/bath/toilet/shower without having to turn off the whole supply. This is just an extension of that principle.

The main argument against more than one actual stop cock is (I assume) the potential confusion it could cause.

However, you would have to turn the water off to do this - which would entail finding the existing stop cock (and we're back where we started).

Theoretically you could turn the water off outside - but, as Mike says, you're not really supposed to touch those.