Thames Valley Police feared Andrew Mountbatten-Windsor might have tried to stop officers entering his home in Sandringham by saying it belonged to the King, according to legal documents.
Senior officers were concerned the King's brother could argue it was not his property, and that separate legal permission would have to be sought before officers could enter it.
Delaying access would have risked the loss of evidence, the force said.
The background to Mountbatten-Windsor's arrest in February has emerged in legal documents, when police asked a judge for warrants to raid the former prince's homes.
Lawyers for Mountbatten-Windsor successfully argued those warrants were unlawful in court last week.
Mountbatten-Windsor's arrest came after the US Department of Justice published material which showed his connections to the sex offender Jeffrey Epstein.
The BBC has approached Mountbatten-Windsor's representatives for comment and he has denied any wrongdoing in relation to Epstein.
The arrest of the former prince, on 19 February, was on suspicion of misconduct in public office.
On 18 February, Thames Valley Police asked for permission from the Central Criminal Court for warrants to search Wood Farm in Sandringham and Royal Lodge in Windsor.
The request included the police outlining the scenarios in which they believed they would need search warrants to ensure access to the properties.
They feared that Mountbatten-Windsor or his legal team would want to see "judicial authority" before allowing the police to enter, the documents show.
The police were concerned that Mountbatten-Windsor or his representatives could argue that the Sandringham Estate was the property of King Charles - and that it would be a slow process getting a separate right of access.
Such a delay would "frustrate the nature and purpose of the search," said the police, in their application for search warrants.
There was also a concern that no one would be present at the property and that media attention could be drawn to the police presence outside while not being able to enter.
Any of those delays could have meant the police would have been unable to gather the evidence they wanted, they argued - and "given the gravity of this investigation", the police asked for search warrants.
In separate documents filed as part of Mountbatten-Windsor's legal challenge against the warrants, he said: "These assertions were no more than speculation."
The documents also detail the type of information the police were seeking inside the properties.
They say: "Paper-work, diaries, business records or other documentary evidence of AMW's [Andrew Mountbatten-Windsor's] time as Special Representative for Trade and Investment.
"Further evidence as to any action, communication, comment or in relation to matters following the release of material by the FBI concerning the late Jeffrey Epstein as AMW will be aware that Thames Valley Police is conducting an assessment.
"Specifically mobile phone(s) and computer(s) [to include electronic notebooks, surfaces, iPads and any older electronic devices," which could have held information about links to Epstein at the time when Mountbatten-Windsor had been the UK's trade envoy."
The documents show the search of Royal Lodge, Mountbatten-Windsor's former home in Windsor, continued until 24 February.
They also reveal his police interview at Aylesham Police Station began at 15:00 GMT and he was released under investigation at 18:36.
The legal documents give details of why the police wanted to talk to Mountbatten-Windsor, including the claim that when he was a UK trade envoy he had forwarded Jeffrey Epstein official reports from official visits to Singapore, Vietnam, China and Hong Kong.
There was also a claim, arising from emails in the Epstein files released in the US, that Mountbatten-Windsor had briefed Epstein on investment opportunities in Afghanistan.
Also mentioned is the suggestion Mountbatten-Windsor held meetings with a private investment firm and then suggesting to Epstein that he might invest in the company.
The legal documents have emerged after a High Court hearing earlier this month in which Thames Valley Police accepted the warrants it used to search Mountbatten-Windsor's homes were unlawful.
Mountbatten-Windsor's lawyers used a judicial review to successfully challenge the actions of the force's chief constable and the Central Criminal Court in the build-up to his arrest.
Thames Valley Police's position was that they had applied for search warrants under section eight and nine of the Police and Criminal Evidence Act 1984 at a hearing at the Central Criminal Court the day before the search.
That court determined that only section eight search warrants were needed and they were granted on that basis - but subsequently, a legal challenge has established that the court should have issued them under the section nine.
But items seized in the raid continue to be held by the police, with a further hearing to take place in 2027 to decide whether the material can be used as evidence.
Meanwhile, the criminal investigation into Mountbatten-Windsor is ongoing.
Thames Valley Police force said it accepted that the "initial court's decision to issue warrants under the specific piece of legislation used was incorrect" before they searched the properties.
At the High Court, judge Mr Justice Hilliard said Mountbatten-Windsor and the police had agreed that the search warrants had been unlawful.
However, he added: "The fact that the search warrants were quashed does not bring the investigation to an end or mean that the whole of the investigation is unlawful."