Cobber

When you say car on do you mean just ignition on or with the engine running?
If it’s with the engine running does the voltage rise if you give it some revs?
The fact that the alt light isn’t coming on with the ignition on / engine not running means you alternator probably isn’t going to charge.
1st thing to do is replace the light bulb for the charge light. To do this you need to remove the instruments to gain access.
Replacing this bulb is much cheaper than replacing the alternator, so it doesn’t matter much if the bulb isn’t the cause of your problem.
The next thing to check is the wiring connections to the alternator, if they’re ok then maybe your alternator has shat itself.