This "fact" appeared on TIL today, and directed me to a wikipedia page, so I was wondering if it was at all a reliable statement!
I addressed this question (along with the related claim that the sultan also sent three shiploads of food aid to Ireland) in detail here:
The tl;dr is that the sultan definitely did gift £1,000; that the claim that he had wanted to give £10,000 first appears in Taylor & Mackay's Life and Times of Sir Robert Peel (1851); and that it is hard to source – the book is not referenced. Taylor was statistician to the British viceroy in Dublin at the time of the famine, and it may be he had access to unpublished information from this source.
A second source, dating to 1894, is more explicit: the Irish nationalist William J. O'Neill Daunt claimed to have heard from the son of the sultan's personal physician that he "had intended to give £10,000 to the famine-stricken Irish, but was deterred by the English ambassador, Lord Cowley, as Her Majesty, who had only subscribed £1000, would have been annoyed had a foreign sovereign given a larger sum…”
Analysis shows the two versions of the tale are probably independent and hence corroborate each other, although O'Neill Daunt was wrong about the amount that Queen Victoria gave – it was £2,000.