Will I need to get some higher specification audio cable to cover that
distance? I want to keep cost down.

The cable is most likely just fine. However beware of
ground loops and other hazards of running audio over
long distances. These have little to do with the cable.

Expanding on that a little:

My "trans-workshop cable" is about 8 metres long and works perfectly. It's
cheap audio cable (shielded of course).

The equipment on both ends is powered from the same electrical circuit and I
don't have ground loop problems. You would have ground loop problems if the
equipment were powered from different circuits. I gather that you are in
the UK (hence "ring" wiring structure, which I like, instead of the American
daisychain) and that everything is in the same room. It should work fine.