If my reading of Woffinden is correct he has the sequence as follows:
1. Hanratty signs the note;
2. Photographs are taken of Hanratty;
3. Gillbanks is sent to Rhyl.
This makes more sense to me, as Gillbanks would need the photos when he made enquiries. It means that he came across Ingledene quite quickly, but all he needed to do was find a guest house with a green bath and a co-operative landlady.
In section 186 of the Appeal, the defence complains that information the prosecution obtained about the Liverpool-Rhyl bus timing was not disclosed. If the 1962 defence team had been investigating for a week they would have found out information like this themselves.