Normally You won't have any trouble running everything off a single 13a circuit or socket even when spindle is under full load or even stalled pulling max amps. But if running direct from mains ring then you have to factor in any other electrical items that can affect and pull high loads. Ie Fridges, Kettles, emerson heaters etc.

It's not uncommon for machines running off domestic supplys to be work fine for months or years then for no apparent reason start locking or tripping breakers. (often it's PC that crashes first) 99% of time when this happens it's nothing to do with CNC machine or it's PC. It's a scaled up kettle or Fridge motor failing so pulling higher loads and the combination pushes the whole circuit over the edge or in most cases the PC PSU is sensitive to power drop and will shut down to protect it's self or lockup.

If your system is running on it's own 13A circuit ie for workshop then you won't have any troubles at all, even with a small/med compressor or dust extractor running.