The PS4 and Imac are directly linked, the BT Vision box uses ethernet plug sockets to connect it downstairs. I'm sorry I'm not too sure which other bits of information from the router you require, what specific field are you looking for?
Advanced stats that may show us some error seconds. Found in Hub Manager, Advanced settings/technical log.
From your original post you mentioned that you streamed and I know you said with ethernet. I know wireless isn't recommended for this but have you tried a test wireless purely to check if issue with ethernet cables etc.
None of the recent home hubs show error seconds any more, the powers that be decided that the customer did not need to know.
You should be able to see them from the BT end, unless they have taken that facility away from you?
hold my hands up to having a moment when advising that one lol.
Trying to rule out internal setup issues as lately have seen issues which sound just like this one and turn out to be extenders/cables.