You have already paid for Windows 7 when you purchased your system.

If you have a Dell Reinstallation DVD then you don't need the product key as it will activate via the inbuilt system locked preinstallation mechanism contained within the Dell Windows 7 Reinstallation DVD.

I will assume however that you won't have one because Dell underwent an OEM Media Reduction policy which seemed to be enforced upon them by Microsoft. You can request media from Dell only if you reside in the United States. As you are from the UK like me; to request media you will have to call Dell and there has been some problems with this. I have made an IdeaStorm idea for Dell to improve their services for Reinstallation media and suggested them to have a global request form aswell as a download link. Please add your vote to it (IdeaStorm unfortunately requires a separate sign in from the rest of the Dell Community): Windows 8 Reinstallation Media IdeaStorm. I did also mention the problem of the faded product keys on IdeaStorm but Microsoft addressed this problem for Windows 8.

As obtaining both the media and lost/faded key has proven extremely difficult in some cases, my Windows Reinstallation Guide and Related Wikies/A Clean Install of Windows 7 instructs the user to install via alternative means. Download a retail .iso from Digital River and user the Activation Backup and Recovery program to restore the Dell SLP Key/OEM product activation that is present on the Dell Windows 7 Reinstallation DVD. The guide explains this process is more detail but note it is an unofficial solution and not supported by Dell Technical Support.