Its actually 6 & 4 landings depending on experience, and if it helps I did my 4 circuits in an N reg aircraft for UK JAA license issue. The instructor was a FAA TRI and an honourary JAA TRI so all perfectly legal.
The CAA accepted the training on an N reg aircraft
As a red herring I had also put my type on my FAA ATP and had a temporary US certificate.
a TRI is sufficient it doesnt need to be a TRE