That's a Weinmann or diaCompe lever clamp (same design for both brands) It requires a special square nut with extensions on both sides which engage the square holes in the band. I don't know if a mail order firm like Wiggle would sell these, but you can walk into any shop and ask for a Weinmann (or DiaCompe) lever band nut.
It would probably help if you removed the band and brought it in with you. BTW this design is somewhat obsolete, so you should probably go to an older bike shop with staff that's been around a while.
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