The wording on the certificate specifies single pilot air transport operations, carrying passengers. Article 157 of the ANO defines, in a rather convoluted way, public transport as the carriage of passengers. It follows that an instructional flight with a bona fide student is aerial work. What may muddy the water is the selling of 'trial lessons' which are actually pleasure flights. The definitive answer can only come from CAA legal department, who are very helpful in such matters. Write to them at:
Secretary and Legal Advisor's Office
Civil Aviation Authority
CAA House
London
WC2B 6TE
Confundemus