UK area code
Stockbridge area code
Stockbridge is covered by 01264 and 01794. It sits across a boundary between dialling areas, so which one applies depends on which part of Stockbridge you mean.
01264The Andover dialling areaSee what 01264 covers →01794The Romsey dialling areaSee what 01794 covers →
If you have the number already, the code it starts with is the answer — that's more reliable than the town name for a place split like this. Look it up.