"registering my fleet in another EEC/EASA state "
You would be caught by the old Article 115 (article 140 in the 2005 ANO) prohibiting aerial work in a foreign reg plane without the permission of the Secy of State (which, as they explain on the DfT website, won't be forthcoming except for specified owner-training cases).
Somebody, "2 Donkeys" I believe, posted on the flyer.co.uk forum recently that he was told by the DfT that EASA aircraft are exempt from this (I think this was in the context of the proposed eviction of foreign reg planes from the UK) but that is not what the ANO actually says. So I would get this in writing first.
My GUESS is that if one could do UK based flight training in any EASA reg plane it would have been done, but I haven't seen it anywhere.
I have in the past managed to get written (and intelligent) responses from the CAA to some suprising questions, but most of the time they will just tell you to get your own legal opinion. This gives them all the options. They can a blind eye (as they do to many things anyway) or they can prosecute, according to whether they want to make a point.