When my dad passed away, I had to cancel all sorts of contracts he had with various companies .. phone, TV, streaming service, home insurance etc. As soon as I mentioned the policy holder had passed away and I was calling to cancel his contracts and pay the outstanding balances owed, I got no hassle from anyone. No questions asked, no messing around, no discount offers, nothing. Every single one I dealt with cancelled the relevant policy's on the spot, there and then.
I know its not ethical to do likewise when that's not the actual case, but then again these companies aren't ethical either. If they don't have a simple option on their websites allowing people to cancel such and such policy, along with the means to pay them whatever you owe them without all the hassle, then no one should waste their time on them imo.
Next time just tell them you're phoning on behalf of the policy owner who passed, and are cancelling their direct debits, please send me the final bill blah blah... and leave it at that. (this is of course assuming you have no intention of opening a new contract with them again sometime in the future!)