The ad blocking software I use "uBlock Origin" does block the chat window, I've just tried it now.
On
https://www.plus.net/home-broadband/contact/ I get a message that says
"Chat to us online
Online chat is currently unavailable, please choose another option."
and the start chat button is greyed out and has no associated action when clicked.
If I turn it off for the plusnet domain and go through this page again, selecting the same items re: product, type of query etc. then the button is not greyed out and I can start a chat session.
Ex - Plusnet Customer (2009 - 2023) now with BT