Debris is a simple cause
Moss, leaves and fragments of mortar can slow water in the valley. On a shallow or awkward detail that may be enough to push water sideways under the covering.
Lining failures are different
Lead valleys can split. Tiled valley systems can crack or move. On older roofs the bedding at the sides may have broken away. These are not all repaired in the same way, so it helps to know what type of valley you actually have.
Check higher up the slope
A stain below a valley does not prove the valley itself is leaking. Water from a chimney, slipped slate or overflowing gutter higher up can arrive in the same area. I would want the roof above the stain looked at as well.
Heavy rain tells you a lot
If the leak appears only in cloudbursts, mention that. Capacity and overflow become more relevant. A drip after every light shower points more strongly toward an open defect.