Woooo, something i know about so i dont have to log on, read, then log off
Depend on how far away your shed is.Like mango I'd use 4 or 6mm but 2.5's fine. e.g- 1.5swa can take 27A clipped direct so 2.5 is fine. Stick a 20A mcb on it and youre well within limits.
Use 3core and sleeve one core with earth sleeving or green/yell tape. This means if you dont get a good connection onto your external braiding you still keep a good earth. Use the earth washer tabs in the gland packs, they are there for a reason

Oh and use waterproof glands, they are pennys more and make a better job.
If your putting a little fuseboard in garage make sure at least the socket is protected by rcd. If your not, make sure the mcb in the house is protected by an rcd. Even better an RCBO.
Also, you do know that any work in 'special locations' is supposed to be notified to building control. Google PartP. Heaven forbid you would ignore it
Check the prices on
www.toolstation.com . Beats my wholesaler most of the time.
14209 SWA Armoured Cable 2.5mm x 25m 3 Core £30.57
99816 Gland Kit CW Exterior 20mm Small £2.57
95003 Cable Cleats 12.7mm No 5 50 Pack £2.68 (cant remember if its no.5 or 6 for 2.5 3core sorry)
27838 Volex Garage Kit IP65 £29.58
77567 MCB 20 Amp SP Type B £2.99
90060 Insulation Tape Green/Yellow 19mm x 33m £0.45
Oh, and make sure your house is earth bonded properly. No point connecting all the earths in the new work if the original caboodle is crap to start with.