running cable from house main board to workshop/shed and gym

The only info I will give is the following... 1. This is not a diy job 2. You need an electrician out to assess & quote 3. You will require an Electrical Installation Certificate 4. It will require notification to Building control.

First of all, do not shoot the messenegr. Second. Do not attempt this yourself. It is illegal to carry out works in a special location, your working external to the home is classed as "outside" even if you are working in another building unless you are a member of a government backed competence scheme. From a practical point of view, you may be able to get the lights and sockets working, but how are you going to test it to make sure that it is safe to use? testing for high loop impedances and testing your RCD's are critical to saving lives. If you know and follow the regulations you are also not allowed to export the earthing system either. You will need to establish a separate TT system at the outbuilding. Membership of a competence scheme unfortunately does not mean you are competent, but my advice as a 50 year old electrical inspector is to get someone in who can do the work safely. If they are not aware of the points I have made, look elsewhere. Dont take my word for it see here http://www.electricalsafetyfirst.org.uk/what-we-do/policies-and-research/statistics-england/