Why water shows up away from the leak
The first thing to understand is that water rarely drips through directly below the hole. It runs along rafters, felt and battens before it finds a low point to drop from, so the wet patch on your ceiling can be a metre or more from where the water is actually getting in. Tracing it back to the source is the single most important step, and the reason an inside fix is so hard to get right.
What you can do from inside, as a stop-gap
From inside the loft you can slow a leak down and protect what is below it. Lay a sheet of plastic or a tarpaulin under the drip to channel water into a bucket, and move or cover anything stored in the loft. If you can see the entry point on the underside of the felt or decking, self-adhesive flashing tape or a roofing sealant can slow it in dry conditions, but it needs a clean, dry surface to stick to, which is difficult during active rain.
Treat any of this as buying time, not a repair. An inside seal does nothing to stop water sitting on the roof covering, and trapped moisture can make rot and damp worse rather than better.
Why the real fix is on the outside
Roofs are designed to shed water from the outside in overlapping layers. A lasting repair has to restore that outer layer, a re-seated tile, new flashing, a patched or recovered flat roof, so water is thrown clear before it ever reaches the timbers. Sealing from inside works against the way the roof is built.
If you have a leak, an internal stop-gap to protect your ceiling is sensible, but book a proper look at the roof itself as soon as you can. We trace leaks to their source and repair them from the outside so the problem actually goes away.
Related service
Roof Repairs
Leaks traced and stopped, slipped tiles refitted and flat roofs patched or replaced, the proper way.