Hospitals in Leeds are failing to meet the target for Accident and Emergency waiting times.
Official Government targets require hospitals to see 95 per cent of patients within four hours.
However, new data shows that 92.9 per cent of patients in Leeds are being seen within this time.
Stats for the rest of West Yorkshire were broadly similar with trusts in Airedale falling in at 94.5 per cent and Bradford, Calderdale & Mid Yorkshire at 93 per cent.
GMB official Steve Rice said: “Over the last few years, time and time again warnings signs have been there that the ambulance service is at stretching point.
“Ambulance workers have had one of the busiest Christmas and New Year periods and we are set to get even busier. The increase in waiting times means that we can’t hand patients over in A&E departments. This means we can’t get back out on the road to get on with the job we do of saving lives.”
GMB national officer Rehana Azam added: “Patients and staff are paying the price for the Government’s failure to manage and invest sufficiently in the NHS. Staff morale is low and many staff are required to come in on their rest days to help deliver care in a service that is massively overstretched.”
Health Secretary Jeremy Hunt said hospital bosses feel they are “running just to keep still” to cope with rising demand.
He told the BBC Radio 4 Today programme: “There is a huge amount of pressure, that’s absolutely clear.”
But he added: “I think we also have to recognise, despite the particular pressures, despite the major incidents - and you always get some major incidents at this time of year - that the NHS is continuing to see in A&E departments nine out of 10 people within the four-hour target.
“That is actually better than any other country in the world that measures these things.”