Pillar drill will be <500W so < 2 amps. Watchmakers lathe will be <1 Amp unless you have fitted an enormous motor!
My workshop (LED Lighting, SX1LP mill with DRO, Taig lathe, couple of watchmakers lathes, filing machine, belt grinder, dremmel, bench grinder, etc, etc, etc) runs off a 13amp fused spur from the house with no problems. You only use one machine at a time typically. Most power hungry device I have is a 2Kw oil filled heater.