Yes I don't think that page is being maintained anymore.
Best to use your favourite search engine's official website such as Google, Bing, Yahoo, DuckDuckGo....
I am unable to search on my bt website using chrome. I have uninstalled chrome and reinstalled but still the same. I have also tried different browsers but still doesn't work.
I think everyone we can safely assume BT are no longer supporting a search engine. The BT page is only fit for accessing your BT account and e-mail.
When trying to use the "Search the Web" fields (enhanced by Google) on pages such as the Email Logon page no longer works and returns no results from the web.
Have BT no longer got Google support for web search.
Interestingly the site is still live if you type in the direct link. They have probably removed references and links to it from elsewhere though. I'm just guessing here.