I can't speak for the British people, of course, but "off of" is a collocation I know is used
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StrazdinsI'm sure Americans use it, but does the British people use it?
Yes, it's quite common in BrE. But some people do dislike it, and it's often regarded as non-standard; so (as Clive says) it's probably best to avoid it in certain situations.
For myself, I have always felt a slight difference between e.g.
1. The ball flew off of the bat.