How much power?
If you need less than 13A you can use a 13A plug in to the house and run a length of
suitable cable to the barn, if it is
protected from physical damage, rodents chewing it, etc, then something like:
Designed for flexibility, capacity to withstand weather, oils/greases, mechanical/thermal stresses
www.cef.co.uk
If it is not protected well or if you plan on burying it then you would need to use SWA (steel wire armour) cable and that needs proper termination with glands at both ends, and from that termination box to flexible cable to the 13A plug in the house.
Achieving selectivity is difficult though, with a 13A fuse at one end you could only use a couple of 5A fuses (at most) at the far end for any ciruits you are planning on to have a good chance of only the end fault taking out its own fuse and not further back to the 13A plug. Even then it is a bit harder to be sure it would not trip a MCB as frequently they trip faster than fuses under certain fault currents.
Ultimately your best plan is to have a dedicated circuit from your CU (consumer unit = fusebox) but that would be notifiable work so you would need to get a qualified electrician to do that and complete the Part P stuff.
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Reading your question again it is definitely
not a DIY thing to do if you are looking at a separate meter, etc.
The proper approach would be a fused switch from the incoming mains, suitably rated SWA cable, and CU in the barn for whatever circuits you are planning. Depending on the current you need, and type of earthing, etc, there are various aspects to calculating the cable size, main fuse size, and the choice of protection in the barn.