TalkTalk don't do free broadband, they have SimplyBroaband at £2.50 so unless they've negotiated a discount they do not have broadband.
Time to log into the Account area of the TalkTalk portal and discuver exactly what the account says for services that they have.
TalkTalk routers have the wireless enabled with the security details on a sticker on them, so connecting using WiFi and phones web browser is perfectly possible..
Re-reading your post you talk about phone in a way that might mean they just have a mobile phone contract? Are they paying for a TalkTalk telephone line? Cost of around £10.50 to £15.40 per month?
A sneaky feeling that someone has a mobile phone with free data.