Thanks for the tag Callum 
The short answer is - it might be possible, but probably not.
Now for my take on the longer response - the CAA define a ‘commercial flight’ as follows:
A commercial operation is defined as: ‘flight by a small unmanned aircraft except a flight for public transport, or any operation of any other aircraft except an operation for public transport;
* which is available to the public; or
* which, when not made available to the public, in the case of a flight by a small unmanned aircraft, is performed under a contract between the SUA operator and a customer, where the latter has no control over the remote pilot or in any other case, is performed under a contract between an operator and a customer, where the latter has no control over the operator, in return for remuneration or other valuable consideration.’
The key elements in understanding this term are ‘…any flight by a small unmanned aircraft…in return for remuneration or other valuable consideration’.
The term ‘available to the public’ should be interpreted as being a service or commodity that any member of the public can make use of, or actively choose to use, (e.g. because it has been advertised or offered to someone).
More info at the following link: https://www.caa.co.uk/Commercial-industry/Aircraft/Unmanned-aircraft/Small-drones/Regulations-relating-to-the-commercial-use-of-small-drones/
For this specific example (Manufacturing plant wanting an update on building progress on a third party building site) my thoughts are:
- If the drone photo is for internal management use only, I’m not sure it falls precisely under the CAA definition of a ‘commercial flight’ - but it might fall under ‘valuable consideration’;
- If the plant’s drone operator is given permission by the building site owner to fly there to take such photos, that sounds ok to me.
However
- The drone operator would of course need to follow the DroneCode in terms of distances to other people / buildings / structures etc
- Workers on the site would need to give their explicit permission to have the drone fly near them
- If anything were to go wrong during filming, would insurance cover be in place?
Without knowing the precise location, my guess would be that the building site lies in a built-up area, which would be the real show stopper, and would mean that the flight would need to be carried out by someone who has Permission from the CAA to operate in such an environment.
Just my thoughts - other PfCO holders feel free to weigh in 