The standard 3 pin UK plug is rated at 13A, so about 3kW at 230V. As part of my 3-phase installation I have a single phase 32A outlet; that can supply 7.36kW. It is possible to get 63A outlets which, at 14.5kW, might just run the compressor.
It could be tricky running a 63A outlet from a standard consumer unit; my 32A outlet comes from a 3-phase distribution box. In general the highest power circuits in a domestic environment are 45A for cookers and electric showers.
So, in theory, it might just be possible to run the compressor on a single phase supply, although how the incoming supply and consumer unit would stand up to it is another matter. It is possible to run a 3-phase motor on a single phase supply via a static converter, but when running the motor only produces about half nominal power, as one phase is essentially unpowered. That may be a problem with a compressor.
As a matter of idle curiosity I wonder how the OP is going to judge whether the responders know what they're talking about or not?
Andrew