Whoah! Careful there Mark!

Legally the answer is "no". You can't use music unless you own the copyright or have permission from the copyright holder. Even situations such as making a back-up copy of a CD which you own aren't simple, the urban myth being that you can do it, the reality being that is is still an offence but the chances of you getting prosecuted are nil.
If you use the music, even at the request of the client, YOU are the one who gets prosecuted, not the client. Since prosecutions are made by a private "company" paid for by the industry, you can bet that they would jump at the chance for such an easy prosecution.

Cover your ass, get a letter from your client to list the music they want and written confirmation that they have cleared any copyright issues, otherwise be prepared to risk thousands of pounds (I'm not kidding, these guys don't muck about) in fines.

Strangely enough I have had the same experience as Mark. If you ask, and it's a non-commercial venture, you usually get a "Well... on this occasion... Okay". If you just go ahead and get found out you risk losing all your equipment (the court can seize anything used in the illegal copying, which includes things like computers) and getting a hefty fine with mega court costs.

Just a warning...