Power Plug/Adaptor for LED Desk Light

Ok so this might be the dumbest question posted here, but here goes.

I took a punt on a LED desklamp from Amazon (more like Alibaba) and when it finally arrived it had a US/Chinese (?) plug with a janky looking UK adapter, for this reason and the fact the lead is too short I went looking for a replacement plug.

Now on the instructions that came with the light were as follows:

POWER SUPPLY:

(Input) AC100V-240V 50/60 Hz

(Output) DC24V --- 0.5A

Whole lamp power 9W Max

Believe it or not this is where I got completely lost as there are tonnes of power supplies / plugs / adapters out there and I know absolutely zero about anything electrical apart from my PC.

Am I safe to buy a run of the mill DC12V (which seems to be the most common)? or does it have to be a DC24V, most of which seem to have a big old black brick attached and look far to overkill for a LED lamp.

Any help so I dont burn my flat down would be most appreciated, thanks.

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