At my previous home I had a cable telephone line and used both cable broadband and dial up internet access via at least two other ISPs on that telephone line for the very rare occasions when Telewest broadband was unavailable.
Admitedly, they weren't Tesco, but that shouldn't make a difference. Dial up internet access normally just dials a specific telephone number, so the supplier shouldn't matter and it will work across any phone line.
I can't see any reason why it wouldn't work with Tesco dial up internet access.
Note: broadband internet access is another issue completely and usually requires a BT line.