Right, I don't think that there's a headset out there that sounds as good as the 555s do (that's if by headset you meant something with a mic built in?).
Your £100 budget puts you in a slightly awkward place TBH. You can afford to upgrade to some brilliant headphones (as long as you go used), ranging from Beyerdynamic's Premium range (DT770/DT880, unlikely DT990 though), Sennheiser HD 580 or HD 600, Grado's upper budget range (never heard these) to even AKG K701s (if you only ever really listen to jazz of classical, and don't do much gaming).
You'd have to buy most of the suggested headphones used though. Whilst this may sound a bit grim, you can hand wash earpads and headband foams of most headphones I've suggested). And here is the the problem - most of the above only really sound their best through a dedicated headphone amp (although some say the Xonar with built in amp is a good stopgap), and some of those headphones probably would leave you a little underwhelmed without an amp.
If you really don't want to but used headphones, then I can't suggest anything that will sound better than HD555s really. There are plenty of pairs of headphones that will sound different, which may be perceived as better in some ways, but ultimately, I'd aim my sights on something used from the tier above.
The best budget headphones in existance bar none, are the Sennheiser HD 580s. Look to pay around £70 for a really good pair (there's some on eBay at the moment, but they look a little nasty to me). They were top of the range reference headphones back in their day, and sound as good as identical to HD 600s.
The other headphones sell for:
HD 600 - £100-120
K701 - £100 - 120
Beyrdynamic DT770/DT880 - £120 - 150
Grados - £whatever they go for
Don't let cost be an indicator of quality. I found my HD 580s to sound a fair bit better than the Beyer DT880/250s that I have as well as the K701s. The HD 600s are better built, but a little less comfortable than the HD 580s, and look a little dated. Decent amps (excepting the Xonar) start at a ~ £100.