Hi Kelly
On the assumption that the injury is "reportable" [which it might not be] you have to decide who the "responsible person" was as defined in RIDDOR Regulation 3:
Responsible person
3.—(1) In these Regulations, the “responsible person” is—
(a) in relation to an injury, death or dangerous occurrence reportable under regulation 4, 5, 6 or 7 or recordable under regulation 12(1)(b) involving—
(i) an employee, that employee’s employer; or
(ii) a person not at work or a self-employed person, or in relation to any other dangerous occurrence, the person who by means of their carrying on any undertaking was in control of the premises where the reportable or recordable incident happened, at the time it happened
On the basis of the narrative as you describe it, it would appear that the landlord remained in control of their pub and all "premises" therein, making places in the pub available for use by your engineer.
The parent legislation, the Health and Safety at Work etc Act 1974 defines "plant" and "premises" in Section 53.....
“plant” includes any machinery, equipment or appliance;
“premises” includes any place and, in particular, includes—
(a) any vehicle, vessel, aircraft or hovercraft,
(b) any installation on land (including the foreshore and other land intermittently covered by water), any offshore installation, and any other installation (whether floating, or resting on the seabed or the subsoil thereof, or resting on other land covered with water or the subsoil thereof), and
(c) any tent or moveable structure;
My interpretation is that the engineer's ladder is "plant" rather than "premises". The ladder is placed within the "premises".
It would be different if e.g. the landlord handed over part of the pub into the control of your engineer, e.g. with a barrier to indicate the area temporarily in the control of your organisation [i.e. your engineer], with you [your engineer] having authority to decide who could and could not enter that area.
But on the basis of my reading of your narrative that has not happened and whoever was in control of the pub [i.e. landlord or their employer] would be the responsible person either as their employer [Reg 3(1)(a)] or if they are self-employed OR if someone argued that they were "not in the course of their employment" at the time of the accident [e.g. if rhe removal of boxes was nothing to do with "work"] as the person in "control of the premises" [Reg 3(1)(b)].
Whether your engineer should have been in control of the area where the accident occurred is a different question! Possibly, but only possibly. You would NOT usually expect each and every area in which your engineer to be working to be handed over to them and as for the area where the accident occurred, the landlord was the keyholder.