If you phoned 03451 720088 at 11am, @Toffi, yes they should have been open [also Live Chat is open now] but you do have to work through various options.
You could try selecting a different number of option if you keep getting cut off - see if it makes any difference! They then might put you through to the right service.
Keep track of contact hours from the list near the bottom of this page:
https://community.talktalk.co.uk/t5/Articles/How-to-contact-TalkTalk-Broadband/ta-p/2230529
They have never advertised 24/7 support for the phone lines.
Even the forum is only 24/7 in the sense that the whole internet is 24/7, and community members can communicate here 365 days a year. It's not staffed 24/7.
Gliwmaeden2, a fellow customer.
From the 29th of March our TalkTalk Community will move to peer-to-peer support and the TalkTalk team will no longer be here to support with queries. Don’t worry we still have plenty of ways to reach out if you need to speak to TalkTalk directly. For more details check out the link in the post at the top of any forum message board.
