I’m not a driver, but as far as I know, there is no outright prohibition on driving whilst taking ANY prescription drug as prescribed, but it is an offence to drive if your driving is impaired by them.
Many drugs, including Baclofen, have a caveat that they may cause drowsiness, and IF affected, not to drive or operate machinery.
However, everyone’s different, and just because something may cause drowsiness doesn’t mean it necessarily will.
Hence, a lot hinges on personal responsibility to judge whether or not you’re affected, and decide accordingly. It’s not dissimilar to deciding whether you’re OK to drive when tired, or if you have a blinding headache.
I think most people can tell if a medication is making them drowsy. If it is, and you decide to drive anyway, you technically commit an offence - although whether you get caught and prosecuted is another matter. It would depend whether you were involved in an accident, or spotted driving erratically.
I know some people feel very zombified on Baclofen. If you’re aware that is you, then it’s obviously not sensible to drive.
If you’re unsure whether it’s making you drowsy, best to chat to your doctor about whether there’s any cause for concern.
I take 60mg a day, and personally don’t feel any more zombified than I did from the MS - but then I don’t drive anyway. It’s not an offence to walk or catch a bus under the influence!