Standard 13A plugs are designed to take a 1.5mm flex at maximum, this has a current carrying capacity of 15A in ideal situations and this level cannot be exceeded because of the 13A fuse in the plug.
In supplying power to a location there are a large number of factors to take into consideration to ensure a safe installation.
The potential current demand of the location, the level of protection required, the current carrying capacity of the cables used, the installation method, grouping, ambient temperature, requirements of the regulations for the location, to name but a few.
Using a spur off a ring final circuit then introduces the considerations of what other power may be used on the existing ring compared to the protective device as well as the current demand for the spur and the requirements for keeping the loading on the ring as even as practicable.
A normal ring final circuit has the potential to be used to its capacity very easily as you can tell from a ring with 10 double sockets this could, at maximum, use 130A if every socket is used to capacity which is way above the 32A protection supplied normally, in a normal domestic situation this does not occur. however with a separate supply attached to the ring a different level of usage come into play and the ring could easily be overloaded, with the potential for fire at the worst and nuisance tripping of the power at the least.
What you are describing with a small consumer unit in your outside building means that the house ring protective device is probably the only one actually protecting the circuit and this can lead to overloading of the cable especially if the cable is not sufficiently rated for the current demand.
The consumer unit being connected with flex is a non standard method and the connection are not designed to accept this cable and may cause problems with secure connection into the consumer unit leading to junctions heating and potentially fire.
I hope this goes some way to explain the problems that may occur in a badly installed arrangement and the reasons why we are not sanguine about providing any form of advice on the use of an untested and incorrectly installed arrangement.