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Think that might be your culprit, have a look at the sides of it to see if there is any printed text that suggests it is a transformer (something like input voltage 240V, output voltage 5V as an example). Assuming it is a transformer, and your old fan was wired to it, then your old fan was a lower power unit running off low voltage. Your new one probably wants full mains voltage, but instead is getting a reduced one and hence won't run.
I suggest looking in the manual of your new fan to see what voltage input it requires. If it's 240V you'll want to ditch the transformer and wire it in directly to the mains.
A multi meter should also be able to confirm if what I'm saying is correct.
Yep, it was already there and supplying the old fan - the new fan didn't come with anything, just the fan unit