A roof leak is rarely a hole in the middle of a sheet. It usually starts at a junction: a flashing that has lifted or corroded where the roof meets a wall, a vent or a skylight, or a valley between two roof planes that has filled with debris.
Gutters have one job: catch roof water and route it to downpipes. When they cannot, the water goes somewhere less convenient.
Blocked gutters overflow, and the overflow typically runs down the wall or back under the roof edge into the eaves. Gutters that have sagged hold water permanently, which accelerates corrosion and adds weight. Downpipes that are blocked or disconnected deliver water to the base of the wall rather than the stormwater system, which is a common contributor to damp problems at ground level.
None of this is dramatic on the day it starts. It becomes expensive when it has been running for a season or two into a wall cavity.
For a burst pipe or a serious leak, turn the water off at the mains tap before you call. If water is anywhere near power points, the switchboard or light fittings, stay clear and treat it as an electrical hazard. Do not enter standing water in a room with live power.