Actually, given what happened afterward, I think it likely the case that the British started the war more to prevent Zanzibar from falling into the German sphere of interest than to end slavery, tho the latter certainly was the justification that was used.
The British had already agreed to swap Heligoland (plus the rights to colonise the mainland) with the Germans for rights over Zanzibar back in 1890, so that was right out. The UK had been trying to suppress slavery on Zanzibar since the 1820s or so, not to mention elsewhere, so it's not like they just took some sudden interest in ending slavery.
They also weren't particularly forceful in ending it even once they'd turned Zanzibar into a complete puppet. I never said that they were uninterested, but it clearly was a priority only when it came to propaganda rather than actual results.
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