Just out of interest - so you are prepared to let them in and search all of your devices for BBC iPlayer or anything that is capable of showing live TV or BBC catch-up? What if they found for example the ITV app on an old tablet - is simply having it installed a crime, or would they have to prove that you have been watching it?
Interesting question. Re. the first part, assuming they found "all of my devices" - I only have a couple of laptops here, one of which is always stored in a drawer out of sight - then that would come down to reading the terms of the warrant to determine whether I'm compelled to do this. It might also be worth asking the accompanying officer to clarify my legal obligations - ideally as a "yes/no" question - filmed so that they can be held to account later if the information they provide turns out to be wrong.
I suspect it would also be worth clarifying the context here - i.e. requesting that they provide evidence to support these demands. As others have said, while TVL constantly imply that the burden of proof is upon the individual to show that they've not breaching the license conditions, in reality it remains upon TVL to prove that you have broken said conditions - with any demand to access your devices to check presumably being predicated upon that. Presumably if they cannot provide proof then there's no case to answer on my part.
As for your second question (which I appreciate might be aimed at a wider audience than just me) personally there's no danger of this since my home isn't littered with "old" devices, nor have any of the devices present ever been used to download software whose purpose is to view streaming content, or will any evidence be present in my browsing history of having accessed any "licenseable" content.
Again, I have nothing to hide - none of my viewing habits fall under those deemed to require a TV license and - worst case, if TVL muppets were granted absolute free-rein to interrogate every microscopic facet of my living space they'd still find nothing incriminating by the definition of the license requirements.
Had the subject initially been brooched by TVL in a respectful and proportionate manner I'd have been more inclined to comply with their "requests". As it stands I'm disgusted by their conduct and simply refuse to reward their greasy tactics by engaging with them.
While I find their tactic deplorable on a personal level, it's disgusting to think of the effects they might have on more "vulnerable" members of society. On that note I wonder how many people with no need for a license have been terrorised / duped into buying one off the back of this behaviour...?
Tbh it reminds me of an experience I had walking to the bus stop after a night out a while ago... with some random dickhead apparently trying to engage me in conversation by repeatedly shouting "yo" at me. With the absolute lack of respect this conveyed I chose to simply refuse to engage while trying to ready myself for confrontation. Had he instead begun with "excuse me mate" or similar; I'd at least have heard him out...