You may conduct training in a N-registered aircraft with your EASA licence within your EASA privileges, since your licence is rendered valid in UK airspace by ANO Article 61. From the FAA regulations, 14 CFR 61.3 validates your UK licence for use in UK airspace.
However, ANO Article 225 also restricts aerial work and therefore remunerated flight training or testing without the appropriate exemption. The owner of the aircraft must apply to the CAA on the form below to obtain an exemption to allow remunerated instruction.
http://www.caa.co.uk/docs/148/201404...W%20V0%202.pdf
You should familiarise yourself with FAA aircraft documentation and regulations (particularly 14 CFR 91) since they differ from CAA and EASA. In acting as PIC you will be responsible for ensuring compliance with FAA, EASA and CAA regulations.
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