The information at the BT Webwise page seems to me to avoid discussing BT's real motives in proposing to employ this system. The quoted blocks below come from BT's Webwise page.
BT Webwise increases your protection against online fraud and makes ads that appear on participating websites more relevant to your interests. It's completely free for BT Total Broadband customers and you don't have to download or install any software for it to work.
This is rather disingenuous. Most modern browsers offer protection against phishing sites. I strongly suspect that most broadband users would prefer to minimise all advertising: certainly this is one reason I use Firefox with its adblock add-on. Of course it's free, BT will be selling our browsing history