You can fly using your ICAO licence which could be a rented aircraft but:
it does not entitle the holder:
(a) to act as a member of the flight crew of any aircraft flying for the purpose of
commercial air transport, public transport or aerial work or on any flight for which
the holder receives remuneration for services as a member of the flight crew; or
By "tuggie" I presume you mean towing. Assuming that those being towed pay for their aerotow, then it is aerial work and you can't do it on an ICAO licence.
Going to Gatwick is not likely to be of much use as the CAA is not there to provide legal advice!