The NHS *shouldn't* leave voicemail. At least, the bit where I used to work had a policy that one does not leave voicemail, since you don't know who will listen to it and thus you can't ensure confidentiality.[1]
Even in today's fast-paced world, customers don't like being greeted with an automated message. According to the New York Times, callers of a certain age are put off entirely if they are answered by a voicemail instead of a real person.

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I have a confession to make: I haven’t recorded a new voicemail greeting since 2014. In the past four years, I (hopefully) have become more articulate, poised, and self-assured. But hear my voicemail recording, and you’d think I was still new to the work world, a little unsure of myself — and probably not an authority. Obviously I need toupdate it. And if you haven’t changed your voicemail greeting in over a year, you’re likely in the same boat. After all, a professional voicemail recording boosts your credibility, makes you seem more competent, and encourages whoever’s listening to it to continue the relationship. A relatively unprofessional one — like mine, for instance — does the opposite: It encourages prospects, recruiters, and potential connections to run in the other direction. With that in mind, I’ve written 18 unique voicemail greetings for every situation. Pick your favorite, practice a few times, then record your new voicemail.