I use to work at the UK CAA, and if memory serves me correct, you'd have to ask for what they call a one-off approval. They wouldn't allow a non JAA TRE unless is was absolutely necessary, i.e there are no JAR TRE's on the type you're wishing to apply to a UK licence (which is of course highly unlikely). If your reason is purely down to you not wanting to go to europe somewhere in a JAR approved TRTO to do the LPC in a JAR sim with a JAR TRE, they'll most likely tell you to beat it.
Either way, answers on prune won't authorise it, you need to get the ok from them.
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