Bonny, due to the "elf and safety" police you need to get part P sign off for any work done in the garden or outbuildings. Theoretically you can do the work yourself if you are a "competent person". Once the work is complete your local council should send someone to inspect it free of charge, but a lot of councils try to make a charge, or will refuse to do it.
I ran 10mm to my garage via the loft to a fusebord and then on to the workshop with 10mm (only because I had to buy a 50m drum). The reason I went for 10mm is that it is running in trunking through the loft and under fibreglass insulation. 6mm would have done the job as far as current carrying capacity but is only rated at 30A if it is run in open air and may have warmed up too much if covered up.
You will definitely need an RCD, either on the main house consumer unit using a spare fuse way for the feed, or better still, a separate RCD/Fuse so you do not trip the house if you have a problem in the outbuildings. A separate RCD/Fuse will involve new tails from the meter and the electricity company will need to see a sign off before connecting it. The feed to the outbuilding should be fused at 30A.
In the outbuilding you will need a two way consumer unit - 30A MCB for the socket ring main and 5A MCB for the lighting.
Don't forget that if you are going underground outside you will need to convert to a suitable SWA (steel wire armoured) and bury it at the correct depth with marking tape above the cable before you backfill the trench.
I am not a professional electrician and no doubt someone on the forum will have more to add. IMHO, when dealing with electricity and potential fire and safety issues, it is better to over spec materials and unless you are confident in tackling the work yourself, it is worth calling in a professional as there are insurance implications and possible issues when you go to sell your house at a future date.
My work was overseen, inspected and signed off by a professional electrician friend.
I know it seems complicated and possibly over the top, but the regulations are there for very good reasons and the risk is just not worth it.
Jim