Does the ALT light come on when the ignition is switched on, before you start the engine ? Also does the fuel gauge etc. work properly ?

Both of these will indicated whether (or not) the ignition supply fuse the instruments is OK. If this fuse is blown & there is no 12V supply to the ALT light, it will behave as you have described.

If the instrument fuse is OK, then you will have a faulty regulator.

Dr Terry