Hmm. Was pondering this earlier as I'd only recently heard the '...and another thing' audiobook featuring Stephen Mangan and Peter Seraphinowizc Serafinowicz as The Book, which didn't quite work for me.
Certainly Briers could have done a great job as he could conjure that same 'twinkle' in his voice as Peter Jones. Of the people who spring to mind who are alive:
Roger Allum
Geoffrey Whitehead
Clive Swift
Anthony Head (too 'smarmy'-sounding? - no offence to him - great voice)
Clive James (too monotonous?)
Griff Rhys-Jones (honestly - think about it!)
David Mitchell ??
Richard Wilson
I think Roger Lloyd-Pack would've been pretty good.
Michael Palin was an early pick for the original, when they were looking for someone with a "Peter Jones-y sort of voice", before they realised they should just get Peter Jones.
Much as I like Tony Head, I don't think he's right for the Book. I think if you were recasting Zaphod, he'd be brilliant, though. Or Zarniwoop, he does a great villain. Richard Wilson might be a good Slartibartfast. I think he has the right sort of qualities to follow Richard Vernon, and Richard Griffiths. And he's called Richard. Works perfectly.
I do think Griff would be a good choice. The trick is not to have anyone who sounds like they're talking down to the listener, just reciting facts about the universe. That's why Peter Jones was so good, he did it straight, there was no condescension to the listener, and he was able to say some of the absurd things that Adams came up totally deadpan. You don't want someone who sounds like they're being funny. Which would be a risk for Griff, but I think he could do it.
If we were looking outside the UK, Andre Braugher could do it. Not just a great actor with a great voice, but he can do deadpan comedy. I don't know how it would go with an American reading the Guide, but he could do it. And if you just want someone with a great speaking voice, well you end up casting James Earl Jones in everything.