Based on the information you provided, it seems like there are two potential sources for the water damage in your kitchen: the roof or the gutter system. Let's consider both possibilities:
Roof: The roofer you consulted mentioned that the felt on the bottom tiles has worn away and a clip is loose. This could be a potential source of water leakage. Even though there is no visible water damage in the attic or your bedroom, water can still travel along the roof structure and find its way to the kitchen area. It's possible that the water is entering through the roof and then seeping down to the coving on the external-facing wall and the corner where it joins your neighbor's property. If the roofer identified issues with the felt and loose clips, it's worth addressing these problems and making the necessary repairs.
Gutter System: The second roofer you consulted mentioned that the gutter sits below the eaves and it would be unlikely for water to jump up and cause the damage. While this is generally true, it's still possible for water to enter the kitchen area if there are gaps, leaks, or other issues with the gutter system. It's good that you've taken steps to address the problem by filling the holes in the roughcast and planning to install drip trays and a new clip. These measures should help prevent any water from overflowing or dripping down the external wall. Make sure to closely monitor the situation after the repairs are done to see if the water leakage continues.
It's important to note that water can be unpredictable in its path and finding the exact source of a leak can sometimes be challenging. Since you've already consulted professionals, it's a good idea to follow their recommendations and address the issues they identified. If the problem persists after the repairs, you may need to seek further assessment or consider consulting a building professional who specializes in water damage or leak detection.
Remember, it's always better to address water issues promptly to prevent further damage and potential mold or structural problems