The NHS is facing what health leaders say is the worst crisis in its history. Hospital trusts and ambulance services across England are declaring critical incidents, and waiting times for admission to accident and emergency departments have reached unprecedented levels.

The Royal College of Emergency Medicine estimates that 300 to 500 people a week are dying as a result of delays to emergency care — a figure challenged by NHS England but endorsed on Tuesday by Sir David Spiegelhalter of Cambridge university, one of the country’s leading health statisticians. “It is quite plausible that hundreds of deaths a week are associated with delays to admission,” he said.

Experts identify a complex set of interrelated factors that have come together to undermine the health service, from concurrent waves of winter infections to a depleted and demoralised workforce.