The Peak Demand figures were produced by the Electricity Association, which ceased to exist after 2003. The load research work that the EA undertook also ceased. The only work on loadings is now done by Elexon and that for load profiling only
Click for profiles. The values for the domestic load are very similar to Profile Class 1 (Domestic Unrestricted).
The demand value of PC1 is the value at the National Balance Point, a theoretrical point on the Grid. If you apply the appropriate diversity factor, you can create the value at each of the voltage and distribution system levels.
For example, the diversity to the meter in a house (on average) is 5, so the MD for a 1.1kW demand at NBP is 5.5kW.
Similarly, the diversity to the LV feeder from the distribution substation down the street is 3.12, so the extra demand on the feeder of adding a house is 3.4kW. The extra demand on the substation is 2.1kW.
To understand these numbers, you should be aware that the definition of maximum demand for distribution purposes is "twice the number of kWh measured in any half hour", i.e. the demand is averaged over an integration period of 30 minutes.
That makes sense for distribution plant with its high thermal capacity, but not for a household and especially not for an individual final circuit within a household. The MD for a household is the near instantaneous MD, only excluding transient loads of switching on incandescent lights and starting small motors.
If you've followed all this and not lost the will to live, you will now understand why a MD of 1.1kW at NBP is compatible with a household MD of 18kW.