Art 16(6) of the ANO
(6) A certificate of release to service shall not be required to be in force in respect of an aircraft to which this article applies of which the maximum total weight authorised does not exceed 2730 kg and which is a private aircraft if it flies in the circumstances specified in paragraph (7).
Art 155
‘Private aircraft’ means an aircraft which is neither an aerial work nor a public transport aircraft;
'Aerial work aircraft' means an aircraft (other than a public transport aircraft) flying, or intended by the operator to fly, for the purpose of aerial work;
‘Public transport aircraft’ means an aircraft flying, or intended by the operator of the
aircraft to fly, for the purpose of public transport;
Regulation 12 of the The Air Navigation (General) Regulations 2006 lists what you can do.
All of this is in
CAP 393
My reading is that you can do it but that you cannot then undertake a PT or Aerial Work flight without a new certificate of release to service from an LAE.
PS. There is no such thing as a "public transport cert SEP" any more. Whether or not it can be used for PT will depend on how it has been maintained.