From my experience, I've never met or heard of a
Jennifer/
Jenny/
Jen from Great Britain. When I was a kid/ teen, we usually were
Jenny. My cousin's wife (the other
Jennifer Marie) is always
Jen, and I'm
Jenny. At work, I'm
Jennifer, or
Jen if a coworker wants my attention. That could be related to the age of the person, though.
Jenny seems to informal for a workplace to me.