No problem with a plastic shed, ilove.
Temporary building site meters and consumer unit are always fixed into a plastic box supplied by the Electricity Company.
I would cut yourself a piece of 18mm plywood, about 600mm square, and simply bolt it to the shed.
Drill the holes through the shed wall and also through the board.
Put rubber washers on the heads of the bolts (outside) to make the holes waterproof.
Screw the consumer unit and possibly some sockets onto the board.
Perfectly safe.
Your most important consideration is proper earthing.
If the shed is near the house, then a normal two-core plus earth type of cable is fine.
If the shed is some way from the building, then it would be better to NOT to export the earth from the house. Just the live and neutral.
Then, sink an earth rod just outside the shed, and connect to the consumer unit.
BUT, you MUST have an RCD fitted as well to comply with earthing regulations.
If you're not too sure, then any electrician would set it up in no time, and test the earth.
I hope this helps.