Peter Smith, who is trained in first aid, said he spent several minutes on hold while a recorded message told him he would be answered in rotation. He eventually drove the child to hospital himself.
Mr Smith wrote to the Prime Minister and Frank Dobson, Secretary of State for Health, after the incident on 17 August.
Severe staff shortages at the London Ambulance Service have led to a computer queuing system being installed to cope with the volume of calls.
Eric Roberts, branch secretary of the public service union Unison, said he was appalled callers had to listen to a recorded message. "I thought that disappeared years ago and there were enough staff to answer calls. No one should have to listen to an answering machine if they ring 999."
Mr Smith said he was called to a neighbour's house in Plaistow, east London, after the boy, Moses Antwi, hit the kerb while cycling and was catapulted through a window. The boy had "blood pouring from his arm" and Mr Smith realised he had severed an artery. He applied a tourniquet and ran back home to call an ambulance.
"I was told by a recorded message that I was in a queue and would be dealt with in rota and not to dial 999 again. I was told this seven times. I could not tell this machine there was a child bleeding to death next door."
Eventually he drove the boy to Newham General Hospital, where he had surgery to repair the artery. When Mr Smith returned home there was a message on his answering machine from the ambulance service asking if he still needed help.
"This is no criticism of the National Health Service, but it just shows there are not enough people working in it," Mr Smith said.
Geoff Martin, director of the pressure group London Health Emergency, said the lack of staff was an outrage. "If this man had not been trained in first aid and applied a tourniquet this child would have bled to death waiting for an ambulance. No one should be left on hold waiting for emergency services to answer - this just proves that the ambulance service is understaffed and under-resourced. Lives could be lost if something is not done."
A spokesman for the London Ambulance Service said it deeply regretted the incident. "We try to maintain the highest staff levels we can. It is a challenge to us how to respond to the increasing number of calls the ambulance service receives."
He said ambulance service staff had called back the boy's family and Mr Smith and were preparing to send assistance when they were told that they would not be needed.Reuse content