Running power cables to garden shed

personally I would use a 10mm armoured cable as people tend to change what they use on the circuit and pull more load. this would have to be fed from your fuseboard and run out to the shed where a small extension board would be fitted to provide a lighting and power supply

Firstly you need to be aware that this work is Part P building regulation notifiable and you therefore must register your intent to carry out the work and get the part P consent from your local building control office. The fees vary but typically are around £200 - £300 depending on the local authority your in. - see link below http://www.donttakethep.co.uk/ No conduit or ducting is necessary if you use a Steel Wire Armoured XLPE cable. and ideally you would be better off using a 4mm cable and fitting a small two way fuseboard at the shed end that feeds two circuits one for lighting and one for power. You could use a 2.5m, but if loaded up to the maximum you will get some volt drop, plus a 4mm cable is not much more expensive and allows you the option of using power in future if needed. All work you undertake must be fully compliant to BS7671:2008 and once completed the building inspector will check and test what you have done and if it passes they will issue the relevant part P certificate etc. You may find its actually cheaper to hire a Part P registered electrician? Alternatively you could take a risk and break the law and not notify the work (not recommended as its a £5000 fine!).

2.5 would be suitable for the loading you describe and at 20mtrs voltage drop is not an issue you could run in conduit , my preference is for armoured. RCD should be incorporated into the design. Main issue here is this is an installation in special location so is required to be either pre notified to LABC so works can be inspected as required or carried out by/under the supervision of a registered electrician who can sign the job off for you. Kevin