What armour cable to use for shed / workshop with at least 8 double sockets?

Hi Tom, The amount of sockets doesn't matter, it is the expected power consumption, cable length, installation method and ambient conditions that matter. Once you have determined the requirement, size the cable accordingly, then protect the cable with the correct protection for your current earthing system. That said, this is an outdoor installation and is therefore notifiable to local building control, failure to notify will give you a £5,000 fine if caught. You can notify but this will cost you between £250-£800. Do yourself a big favour and get a PartP registered contractor to view your existing installation, select the correct installation method and notify on your behalf for £1.50 if the job gets done.

To be able to calculate the cable diameter required, the distance from the house to the shed is needed. However as a rough guide it would be sensible to have a 40amp BSEN60898 type B MCB at the supply (house end). This would allow for a 32amp ring circuit for the sockets and a separate 6amp lighting circuit. For a 40amp supply a 6mm or if a longer run 10mm SWA cable would be required. If the incoming house supply is PME (TNCS) then a 2core SWA cable should be used with a local earth electrode driven into the ground at the shed end making the shed submain a TT supply. If the incoming house supply is TNS, then the earth can be exported and a 3core SWA would be preferable with the third core used as the CPC and cross bonded to the outer steel wire armouring. It must be stressed that this is Part P notifiable work. So if you are doing it as DIY you must pre-register your intent and pay your local authority Part P notification fees upfront. (Typically around £200 - £300). Best advice is for safety and to save money hire a professional electrician to install it, as installing and testing the work requires specialist equipment. (e.g. EFLI and RCD tester etc)

when you mentioned compressor.... I'd use at least 10.0mm 3 core armoured run of a 40amp or bigger MCB straight from your main consumer unit inside the house. For a accurate answer we would have to take into consideration the draw you need and then work out a voltage drop over the length of the cable.