In order to get a supply to your barn you will need to contact, initially your proposed supplier (e.g. eon). Explain to them what you require and they will then redirect you to the relevant body in your area.
In order to get a supply to your property a survey will need to be made, in order to ascertain where the nearest suitable supply feedis in relation to your barn, generally this is in the area of the nearest road where there are other properties with existing supplies.
After the survey has been carried out you will recieve a quote for the cost of laying in the supply and conditions which must be met in order for that supply to be installed. These will include a trench must be dug, to their specifications, from the border of the public highway, where the supply point is, to the barn premises or they may require postholes to a set specification. They will also require copies of permissions from any landowners whose property the supply cables will cross.
In some areas they will give the option for them to carry out the "civils" and a price can be requested from them if this is the case.
Having a mains supply installed is not a cheap business and realistically, if there is a substancial cable run required it is generally worth the additional cost to have a three phase supply (400volts) installed.
Hope this helps.
Tony.