So having decided to take my own advice, I set about trying to find somewhere that I could flex my reviewing muscles, half-way between the publications aimed at the teaching professions, which I already review for (and which 'don't count' as academic publications, as we learned from Geoffrey Walford below), and the scary world of real academic publishing.
What I found was ESCalate, the Higher Education Academy's subject centre for Education, if that isn't tautologous. That is to say, it's the bit of the HEA concerned with Education Studies at universities, with the purpose of improving teaching and learning in that subject. The exciting thing is that once your registration with ESCalate has been approved (which I assume is someone somewhere going "Yup, definitely someone to do with education. She's okay.") you can volunteer to review any of the books they have available. After which they send you the book and give you a month to submit the review. And there you have it, a almost academic publication. Certainly enough to give me a boost.
So if you're interested in the city academies programme, you might be interested in my review of The Great City Academy Fraud by Francis Beckett. Then perhaps, you might be interested in getting hold of your own book to review...there's some interesting looking new titles!