This may not be of much use to you, but I use JSTOR to search for book reviews. Under the advanced search options you can filter for reviews and it turns up quite a few results. The problem is, you really need access to an academic library as most of those reviews were published in journals and if you don't have digital access to those journals you can't read them. If you're in university that's usually not a problem, but I understand that most people are not.

Sometimes just googling 'Book Title Academic Review' will turn up a result, but usually it does not.

For my field (medieval military history) the website DeReMilitari.org posts reviews of books every so often which are very useful, and usually written by academics. They don't cover every book but they do include quite a few. I'm not sure if there are equivalent sites for other areas of history, though.

I agree that JSTOR and other databases of academic journals are the primary way to find reviews. With certain more high-profile academic authors who often work for a more lay audience, you might find some reviews in the New York Review of Books and the London Review of Books.

Depending on where you live, you may be able to access JSTOR without being affiliated with a college or university. In the U.S. many academic libraries, especially those attached to state schools, are open to the public. If you can gain access to their computers (as an example, my alma mater, the University of Maryland offers guest library logins), you may be able to access some of the databases to which the library subscribes, including JSTOR.