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Most hire shops have jacks of differing types.
Depending in the shed construction, though, lifting it unevenly, or without enough supports, may have it pulling itself apart.
If you do lift it, you could slide under some a pair of treated 4x4s as skids, with a DPC strip between the skids & base (passing there's a concrete base).
Otherwise, maybe concrete pier blocks?
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Levers would be your friend here. Get some extra floor bearers and sit the shed on those. My shed sits on top of bearers that have some damp proof course roll on top of them.
I have plenty of pressure treated 6x2 joists, could rip those down to 2x2 batons to be used as bearers. Stick those under the shed perpendicular to the existing floor bearers/joist, maybe even throw some damp proof course stuff over the new bearers and Bob's your mother's brother.
How wide is your shed?
If someone needed to raise a shed, perhaps because they'd noticed the base on the exterior was damp, where could someone hire such a jack?
And what would they put between the base and the concrete base it's on?