You cannot have multiple ISPs set up on an ADSL enabled phone line. I am not aware of any reason why your computer itself cannot be used to connect to different broadband services, particularly if a router was being used. With a router, it's just a matter of connecting to it and you're online.
Tesco BB, in any case, is very expensive for the speeds and bandwidths provided; Tiscali's 1MB unlimited at £12.99, 2MB unlimited at £14.99 or up to 8MB unlimited at £17.99 is probably as cheap as you can get, apart from TalkTalk's Talk3 International offer.
You can also use a dialup modem service and a BB service on the same computer.
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