Well, I think this is an important subject and I don't claim to know the procedures inside out but you will have heard about 'chain of custody'. For those who don't know, the term denotes the way in which the handling of an exhibit is tracked from collection at the scene all the way to production at court so that if anyone ever asks how we know that bullet is the one that was found under the sofa (or whatever) there will be an answer. The longhand answer would entail putting each witness who handled the item in the witness box in sequence and getting each one to say how and when they acquired the item and what they did with it.
Obviously, such a system is not going to depend on memory so there needs to be a paper record and that record should obey logical and consistent rules that don't vary from case to case, item to item, or witness to witness.
So, to start with, the witness who collects an item will assign an exhibit number consisting of his or her initials and a sequential number - PV1, PV2 etc. When the exhibit is handed over, say to a detective, it will need a further annotation, I'm not sure what, but it should be something that makes clear the detective was not the first finder. So, thinking further along, if an exhibit is going off to the Home Office lab, it makes sense to use a form detailing the sender, describing the item, giving a date and stating what information is required. The duplicate (or triplicate) copy that's sent back is the receipt and evidences the chain of custody.
We would need to see the relevant manual to follow all the steps but it's not hard to see what the essential are, or that there is nothing inconsistent about Peter Vanezis 'producing' exhibits in a witness statement which then go somewhere for testing under cover of a specially designed form.