Luckily I read the small print before whipping out my internal modem and bunging it in the post because it seems that Pipex are taking only working external modems.
Here is the wording of the advert
"Any customer placing an order for the Xtreme Solo service between 14th May 2002 and 13th June 2002 is invited to send their old (working) external dial-up modem, plus power supply and cables, to PIPEX and exchange it for a brand new Fujitsu FDX310 ADSL modem (excluding micro filters) worth £94"