Depending on what cable it is and on the length of the run, that 1.5mm^ say if it was SWA could have a 16amp protection device, if it was a really short run it may even go to 20amps. So the first thing is to calc the actual load that cable can take and see where you are.
So for argument sakes let's say you can uprate to 16amps. I would then fit a small 2 way enclosure fitting a double isolator with a 6amp protection device for the lights and a 10amp protection device for the socket inside the shed. The protection devices would depend on what is protecting the original supply. If that 10amp device is on the rcd that prtoects several MCB's then I would move it to the non protective side and fit a 10/16/20 amp RCBO as the cable is buried. If the cable is SWA and it is 3 core with a dedicated CPC then you need only fit an MCB, even if it's buried.
So the shed protection devices would be RCBO at main CU...........MCBs, if it MCB at the main RCU then RCBOs in the shed. IMO if it was posibble I would MCB at main board and RCBOs in shed as that would give you a better installation regarding nuiscience tripping.
As this is in the garden and therefore a special location you would need to either notify this work or get an electrcian in that is part of a self certification scheme. Aslo all this work would need to be tested and certificated and again I would suggest getting someone in to do it if your not a qualified electrcian.
