There is no consensus on this issue and Licensing Authorities deal with it differently.
When Licensable Activities are provided, the Licensing Act requires that the holder of the premises licence must ensure that the licence or a certified copy of it is kept at the premises in the custody or under the control of-
(a) the holder of the licence, or
(b) a person who works at the premises and whom the holder of the licence has nominated in writing for the purposes of this subsection.
In addition, the holder of the premises licence must ensure that-
(a) the summary of the licence or a certified copy of that summary, and
(b) a notice specifying the position held at the premises by any person nominated to hold it are prominently displayed at the premises.
Broadly, this means that, if the Licence holder is not around, the licence, or a certified copy of it, is given into the custody of someone else to produce to the Police or anyone else who requires to see it.
The confusion arises because the Act does not make clear whether the notice identiying that person is required only in the case where the Licence Holder is not there or, alternatively, al all times.
To fail to display the required notices is an offence. If you are told to put up the Notice, why not do it but I have to say that this approach is very pedantic.