What the underlay actually does
Underlay beneath slates or tiles is a secondary layer. The outer covering should shed almost all rain. Felt helps with wind-driven moisture, dust and occasional water that gets past the covering, then directs it towards the eaves.
If water is regularly running on the felt, there is usually an outer-roof defect worth finding.
Common signs from the loft
Older bituminous felt can become brittle, especially close to the eaves and around nail holes. Tears may be visible around previous repairs. Sagging between rafters is normal to a degree, but deep pockets can collect water.
Modern breathable membranes behave differently, so the age and material of the underlay matter.
Why inside patches are limited
A patch applied from beneath cannot usually be lapped properly beneath the tiles above. Water running down the top face can simply pass behind it. Inside repairs may reduce a drip temporarily but they do not recreate the intended layering of the roof.
Where the covering is lifted for a proper repair, damaged underlay can be dealt with from above over a sensible area.
Eaves deterioration
The bottom edge often deteriorates first because it is exposed to light, moisture and movement around the fascia. If it no longer reaches the gutter, an eaves support tray may be appropriate depending on the roof.
The tray must integrate with the existing underlay and drainage. It should not be treated as decoration tucked under the bottom row.