I could see an argument for relaxing that for mobile voicemail, on the basis that mobile phones are pretty personal and not generally shared by multiple people, but I've no idea whether that may have happened. Or, indeed, whether such policies may vary between organisations within the NHS.
I don’t mind it so much for people I know. I have to deal with them on a daily basis, so I can’t hold voicemail grudges against them. However, if someone cold calls me or it’s just an acquaintance that calls, a crappy voicemail annoys me and leaves a bad impression.

When setting voicemail for a busy day, remember to: Always begin with an introduction. Start with your full name followed by the official name of your salon. This assures your customers that they have dialled the right phone number. If you have more than one salon, specify which one they reached (“It is Day Spa Dahlia on Green Lane, 17” ).
As a real estate professional, you're always on the go. Whether showing homes and apartments to a prospective client or staging a home for sale, it's likely that you're out of the office quite often. Anyone in the industry knows that, out of the office is a good place to be. Unfortunately, it makes staying professional just a little bit harder. What happens when you're working with one client and another one calls? Most likely, you send that call to your voicemail box, but what does your voicemail greeting say? What should voicemail messages include? If you're voicemail isn't offering the right information, you might lose a sale.