What affects how quickly an emergency plumber can respond?
Current job load, time of day, distance to the property and how the emergency is described when you call all affect response time.
Response times aren't fixed - an engineer already on a job nearby responds differently to one starting from further away, and call volume genuinely varies by time of day and season, with cold snaps a common trigger for a spike in burst-pipe and heating call-outs. Describing the problem clearly when you call, including whether water is actively escaping, also helps whoever's coordinating call-outs prioritise correctly.