Ordered a voltmeter to check but I did find quite a few posts talking about the alternator power steering problem. Pretty sure it's not belt driven and is just all built into the steering column. How difficult is a new alt to fit? Looks relatively simple
If the light's on whilst it's running it's likely to be the alternator.
You need to stick a volt meter on the battery. It ought to be 13-14v with the engine running and 12-14v with the engine off.
If it's lower when running it's the alt if it's lower switched off it's the battery.
Is the steering defo electric? If not it might be the belt that drives the steering pump also driver the alternator and is slipping or broken.