UK area code
Caldicot area code
Caldicot is covered by 01291 and 01633. It sits across a boundary between dialling areas, so which one applies depends on which part of Caldicot you mean.
01291The Chepstow dialling areaSee what 01291 covers →01633The Newport (Gwent) dialling areaSee what 01633 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.