An overwhelming majority - 73% - say that Prince Andrew should be investigated by the Met Police, over allegations of sexual abuse. Just 13% say he shouldn't.
The poll comes after further revelations and accusations have been released by a court in the US.
The poll also showed the monarchy has lost its popular mandate, with just 48% preferring the monarchy to an elected head of state.
That's a drop from 57% last April.
Campaign group Republic is also challenging the Met to step up and investigate Andrew on the strength of numerous allegations.
While some offences are alleged to have taken place in London, UK law also allows the prosecution of offences committed overseas. The recent documents reveal accusations that Andrew had sex with underage girls while visiting Jeffrey Epstein's island.
Speaking for Republic, Graham Smith said today:
"Clearly the public have serious concerns about the conduct of the Met police and feel Andrew should be investigated. Numerous other cases against celebrities have led to interviews under caution and prosecution, yet the police have done nothing about Andrew."
"Just last November Russell Brand was accused of various sexual assaults - which he denies - yet he was rightly interviewed under caution. So why has the same not happened with Andrew?"
"There is the sense that the Met are giving the royals preferential and very lenient treatment. They refused to interview Charles when facing cash-for-honours accusations, they ignored Charles accepting three million euros in cash and now they continue to ignore very serious accusations against Andrew."
"The police excuse that they are waiting for fresh evidence is spurious. So far they haven't investigated the case beyond looking at some documents, they haven't sought that evidence or sought to interview Andrew or other witnesses."
"It's time for the police to act. Now."
Methodology: Savanta interviewed 2,281 UK adults aged 18+ online between 5th and 8th January 2024. Data were weighted to be representative of the UK by age, sex, region, and social grade.
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