The modem is simply the way the computer accesses the phone line. A single line with jacks (all to the same line) would work (here in the U.S., anyway) as long as one computer at a time uses the line, via the modem.

Setting up a free email program and taking a few weeks to forward everything that comes in to the dedicated address (and send a change of email address to all senders) would then allow the one with the dedicated email to be free of whatever IP company you choose. Yahoo.co.uk, for example. Gmail.com (if you need an invitation to join, I haven't used more than about 3 of my 1000 I can send out).

SRS