FAA complex rating counts as differences training?

[Zonkor]

I have an FAA complex rating for ASEL-category airplanes (essentially equivalent to SEP in EASA-land). I also have an EASA PPL (SEP). The UK CAA is my "competent authority".

Question: Can I fly airplanes with constant-speed propeller on my EASA license?

In other words, does the FAA complex rating count as differences training for the CAA, or do I need to do differences training again with an EASA instructor (and get a logbook sign-off)?

Thanks

[Whopity]

You need differences training to be signed by an EASA instructor before you can exercise the privileges.

[Flyingmac]

What if you were flying something complex or high performance before JAA existed, let alone EASA? Surely privileges aren't removed?

I'm in that situation. Nothing in my log books except the flights themselves.
There was no requirement for any sort of sign off. I'm wondering if I'm safe to continue flying so called 'Complex' types.

[flybymike]

"Grandfather" rights apply to those with complex experience prior to the JAA/EASA "invent extra regulations and jobs for the boys fest."