Older small cars are often under serviced and over used so take your pick of what manufacturer's parts you want to deal with. For starters look at doing, new oil, new coolant, new filters, new suspension, new brakes, etc, etc. If not now, they will be going fairly soon. Goes with the territory of older small cars.
Lots of other makes use the same steering system. Its electric, so for any problems first check the battery.
Symptoms:
Cuts out on full lock - current demand goes up, weak battery allows volts to drop, steering trips. OK when engine restarted.
Cuts out after a cold start on a cold morning, Same issue caused by weak battery not coping with starting car and all the other demands of cold weather.
Cuts out randomly might be a battery with internal short but steering might be faulty
Pulsing or kicking back - might be a steering problem.
Reconditioned columns are £180. Dont buy new.
Get the battery properly stress tested as it likely to be too small and worn out. Replace with the best you can.