I have had power installed to my shed some years ago and have only now noticed that the fuse fitted by the electrician on the main board only gives me 16 amps and I have just purchased a Plasma Cutter that requires 40 amps, 32 amps minimum and was hoping I could change the 16 amp fuse for a 40 amp on my main board without any problems.
The purpose of the fuse, (yours is probably a miniature circuit breaker MCB), is not to allow power to supply whatever equipment you want to connect to the circuit..
Rather it is there to ensure the cables supplying your equipment are NOT damaged by the power that your appliances need..
The basic concept is something along these lines..
Electricity ALWAYS generates heat as it flows around a circuit..
More current = More heat..
Cables carrying more current will need bigger conductors compared to cables carrying less current..
Bigger cables cost more money..
Most jobs are designed for the most cost effective balance of power required -vs- cost of the cables needed..
As a general rule it is unlikely that most circuits could have their current carrying capacity more than doubled without some new wiring installed..
The weakest link MUST be the protective device NOT the cable..
Otherwise you will just end up melting your cable!!
There are other problems such as Volt Drop, & earth loop impedance which also need to be considered..
So without knowing exactly what size cable is currently installed and how far away the shed is..
it is impossible to say 100%.
But on the balance of probability it is very unlikely you can safely just uprate your 16A MCB with a 40A MCB.
:coffee