I have here a print out of LAA document TL 2:09.
"Learning to fly in a LAA aircraft is quite legal, but the following conditions apply.
1) Training towards EASA & non EASA licences or ratings is permissible, & flight time conducted in LAA aircraft counts rowards those required under EASA towards licence or rating issue, renewal, or revalidation.
Initial Licence or Rating
2) An owner may recieve remunerated (or un-remunerated) flight training towards an initial licence or rating in his own LAA aircraft provided he is a "sole" owner & not part of a group ownership."
etc, etc.
Try getting in touch with LAA. By the way, yes second hand LAA a/c are perfectly safe. Mine was built 1959 & has just received it's permit yet again. Similar a/c can be had for ~£12k.