Money Saving Expert did some experimentation and found that the recent popularity of the Ice Bucket challenge - which pushed an awful lot of videos into people's timelines - has been responsible for a greater number of users busting through their data allowance and having to pay additional fees as a result.
I've discovered that the issue exists on my iPhone - where the default setting is to always auto play, and for my Android running Xperia this is also true. For those not using the Facebook Beta app on Windows Phone the issue is moot. (An example of a missing feature turning out to be a benefit?)
The Money Saving Expert article includes details on how to disable auto play, if you use Facebook on your mobile it's probably worth doing.