Ambulance managers are investigating a delay in sending an ambulance to the scene of the crash and a 24-minute hold-up alerting the police.
One witness said it took paramedics too long to get to the scene.
Yesterday, the length of the delays were confirmed by both emergency services.
The first 999 call was made to the South Central Ambulance Service at 12.28am on Sunday but it took six minutes for controllers to dispatch an ambulance.
The first crew reached Westbury at 12.50am. The police were not alerted by the ambulance service until 12.52am - 24 minutes after the first call. Officers arrived 10 minutes later.
A woman who works as a chef at the nearby Reindeer Inn said: "We waited for almost half an hour for the first ambulance to arrive and kept saying 'where are they, where are they?'"
Ambulance service spokesman Alison Brumfitt said an investigation was under way and that the nearest available paramedics had been sent as quickly as possible.
She also added the length of time taken for the service to notify the police was currently being investigated.
Ms Brumfitt added: "More than 100 999 calls were made to the Oxfordshire and Buckinghamshire control room between midnight and 1am on Sunday.
"This is an extremely high volume of calls and more than double the normal call volume experienced at this time."
The incident comes just over three months after an ambulance was wrongly sent to Grove, near Leighton Buzzard, in Bedfordshire, instead of Grove, near Wantage, because of a mix-up in the control room.
Thames Valley Police spokesman Marianne Shaw confirmed the timing of the notification about the crash from the ambulance service but refused to make any further comment.
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