As Chuck has indicated, copying a CD for 'back-up' purposes (or ripping files from your own CD so that you can listen to them on an MP3 player) is technically illegal in the UK. (This country doesn't have the 'personal use' loopholes which are built into US legislation).
However UK courts are obliged to consider the concept of 'fair dealing', which has no statutory definition but examines the economic impact of any copying which is done. So it's not only extremely unlikely that anyone would ever be brought before a court for simply copying their own CD (for their own use) but even more unlikely that a court would act against the person who copied the CD.
Incidentally, if you're REALLY worried about the technicalities of copyright legislation, I hope that you wipe or destroy any videotapes or disks, upon which you've recorded TV programmes, as soon as you've watched the programme. It's only legal to make such recordings for 'time shift' purposes. Retaining the recordings afterwards is illegal!
Chris