This is all conjecture, you may well be right, but I don't believe that a contractor is considered an employee for this sort of thing. If I contracted you for some research and the secrecy of it was it important to me then I would certainly put that into a contract, so that if you gave it to anybody else you would be in breach of contract and I could prove it in court.Confidentiality, copyright and IP are different things, as an employee the employer demands/owns all of these for the work you do whilst on their time.
As a consultant, Confidentiality is demanded by the customer, as is any privileged information within the work you do, copyright and IP is different as certain parts (e.g. style of the report etc) may be owned by you, but much of the content will be owned by the customer - often a contract will make this clear to clear up any ambiguity.
A contractor, as far as I understand is often considered as an employee in terms of these sort of things - i.e. all work done has been paid for specifically by the customer and they own everything, perhaps not as that isn't an area I know well, in terms of confidentiality it will always be with the customer. (it would be seen as a huge breach if you contracted for one party and then passed confidential to another.
Long time since I took advice on this, I generally work in line with the advice I was given then though; as a consultant the customer owns everything specific to their job, but I would own my style of reports/documentation/calculation methods etc.
In terms of an EICR I would see that as the confidential data and conclusions within the report are privileged, but the report format/boilerplate were mine - I would have thought similar for a contractor in this respect as you would already have the boilerplate and report format when you start.
I do know that if I was a photographer and you paid me to take a photo, I'd take the photo and give you the printed photo or digital file, but unless it was stated otherwise in a contract I would own the copyright of the photo