The rave lasted from Saturday night until Sunday afternoon.
Avon and Somerset police said they first received calls of an illegal gathering at Charmy Down airfield, Bath, at 11.21pm on Saturday night.
However, when officers arrived ten minutes later, they found roughly 1,000 people had already gathered at the event, and further resources were called.
The service said a risk assessment quickly concluded it would have been unsafe to have intervened at that stage, and officers decided the event should be contained until daylight.
Officers also had to attend other emergency calls in the area, which left resources too strained to shut down the event immediately.
Police said although roads had been closed off on approach routes to the field, rave-goers were abandoning their cars and making the rest of the journey on foot.
Mounted police patrol the Glastonbury festival in 2009 – also near Somerset.
The music was eventually turned off at 1pm on Sunday, and the site mostly cleared three hours later.
Even then, officers said they were still dealing with a group in a nearby field who were trying to continue the rave even longer.
Yesterday evening, Avon and Somerset police confirmed there had been five vehicles seized from the event, as well as a power generator and other equipment.
There was also one arrest after a person refused to leave the area after the rave was dispersed, and it is understood police are appealing for information to identify the event organisers.
Police said they did not have enough personnel, and shutting down the rave would have been too risky.
Avon and Somerset police said: “A full risk assessment last night concluded the potential risks to public safety of an intervention to close an event attended by more than 3000 people in dark and wet conditions were too great.
“There were also other significant incidents across the force area including 120 999 calls which required an immediate police response and the attention of our resources. Therefore, the decision was taken to contain the event until daylight hours.
“We had the first report of a potential unlicensed music event near Bath at 11.21pm on Saturday 18 July.
“Officers attended within 10 minutes, quickly established there were already several hundred people at the location – the former Charmy Down airfield, Upper Swainswick – and called for further resources.
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The music wasn’t turned off until early afternoon on Sunday.
“Officers closed off the approach routes, however people were abandoning vehicles and making their way to the site on foot. Officers were still turning vehicles away at 6.40am today, Sunday 19 July.”
The service’s Chief Superintendent Ian Wylie apologised to local residents for the disruption caused by the event, adding it was a “frustrating” experience.
Chief Supt Wylie said in a statement: “It’s frustrating that we are having to pull officers away from our 999 response to deal with the selfish actions of the organisers of this event and those attending it.
“They knew full well the disruption this would cause and the ongoing risk to public health of large gatherings due to COVID-19. We brought officers in from their rest days and called on support from neighbouring forces to close down this event.”
The incident occured at an RAF airfield near Bath, pictured.
Avon and Somerset police received mixed responses to the way they dealt with the incident on their social media pages.
One user on Twitter wrote: “I understand that you did not have manpower to actively disperse the crowd. But you could have put on ear-defenders, tracked to the speakers, pulled out the power, and cut off the plugs. Crowd would then probably have dispersed itself.”
Another wrote: “Shabby job. 13 hours to shut down a rave. You should be ashamed.”