Thanks to the eagle eyes of 23er Gigi, we've discovered a couple of complications with changing your email address on Google and Blogger.

No change email option
Some people may not see the 'change email' option next to 'security' on their Google Account screen.   If you don't, then the only way to do it is to remove your old email and add the new one separately.   In this case, do click the 'edit' option underneath your email address, and scroll down the screen to where it says 'add an alternate email address to your account'.   Type your new email address in the box and click save.   You will be sent an email with a link to click on to verify in the same way as for the other method.   You can then return to the same screen (following the steps above), only this time click 'remove' next to your old email address.

Blogger profile and blog authors
Changing your email on Google unfortunately does not update your Blogger profile, so this needs to be done separately.   Sign in to Blogger, and click on 'edit profile' under your name (and beside your photo if you have one).   In the 'identity' section you should see your new email by 'username', but your old one in the 'email address' box.   Delete this and enter your new one instead.   Scroll to the bottom of the screen and click 'save'.

Thanks again to Gigi for spotting these - if anyone else encounters unexpected things when changing their email, or notices somewhere that hasn't updated, please let us know!

(Edit: And thanks to the eagle eyes of Alison, the title of this post is now correct!)