Firstly I would say that running twin and earth outside is not acceptable. The whole installation should be in armoured cable, properly terminated at each outside connection, IMHO.
You might also need to take extra care with the earthing arrangements at the outside locations, depending on the earthing arrangements used at the main supply to the property. You don't want that electric fence to be too effective in the event of a fault!
How many sockets do you already have on that outside spur, what current is it rated at, and how is it supplied from the property? Is it RCD protected? It sounds like a single spur is providing for the outhouse, a couple of sockets in the garage, a couple in the shed, a couple in the chicken coop, some security lighting too.. plenty of loads have been tacked on to that circuit already and there is mention of it being fed from a lighting circuit. Alarm bells are ringing at this stage.

As to why you have no output at the additional socket, though, it must be down to a simple wiring error. Either incorrect connections (if 3 phase cable is used for a single phase supply the colour codes will be wrong so be very careful that you have identified live, neutral and earth correctly) or a connection not making contact, possibly inside the socket itself. You can often get readings that look OK on a multimeter with a high impedance input, despite one of the connections actually floating.
I would, however, urge you to make sure that the
whole installation is sound, noting the (not necessarily exhaustive list of) points above and employing an electrician to do so if necessary. I'm not an electrician, BTW.
