A roof that has lost tiles in a gale or split at a flashing during heavy rain is a problem with two halves: stopping the water now, and repairing it properly later. Doing the second badly because the first was urgent is how people end up paying twice, so the useful thing to know is what a legitimate emergency response looks like and what it should cost.
The first hour, from inside
Move what can be moved, put a container under the drip, and if a ceiling is bulging with trapped water it is safer to pierce it deliberately in one place over a bucket than to let it come down as a sheet. Turn off electrics to any circuit with a wet fitting. Photograph everything, dated, before anything is cleaned up, because that is what an insurer will ask for. Nobody should be climbing on a wet roof in wind to look.
What temporary covering actually is
A legitimate emergency visit makes the roof watertight without pretending to repair it: a tarpaulin dressed over the ridge and weighted or battened, a slipped tile relaid, a split flashing sealed. It buys days or weeks and it is priced as a call-out plus materials. A contractor who proposes a full re-roof during a storm, at night, for cash, is not making the roof safe, and the pattern is common enough after named storms that it is worth naming.
The insurance half
Storm damage is normally covered by a buildings policy; gradual wear is not, and the argument between the two is what your photographs and any dated survey settle. Most insurers expect you to take reasonable steps to prevent further damage, which is what a temporary repair is, and will usually pay for it. Tell the insurer before commissioning a permanent repair, because a job done first and claimed afterwards is the one that gets queried.
Questions people ask about emergency roof repairs
Will an emergency roofer come out at night?
Many will, and the call-out rate reflects it. What they will do at night is make it watertight; the diagnosis and the permanent repair wait for daylight and safe conditions.
Is storm damage covered by insurance?
Sudden damage from a storm normally is under a buildings policy. Deterioration that was already underway usually is not, which is why dated photographs and any earlier survey matter so much to the outcome.
How much should an emergency roof call-out cost?
It is priced as a call-out plus time and materials rather than as a job, and it should be quoted that way before anyone starts. A demand for a large cash sum up front, in the rain, is the signal to stop.