Only 42% of Britons back Prince Charles as their next King, according to polls.
The findings were uncovered in a ComRes poll for the Independent.
More than half (52%) of Labour voters at the last election believe the Royal Family should skip a generation and make Prince William King when the time comes.
Prince Charles is, however, more favoured to take the job by Conservative and Liberal Democrat supporters, with just 35% and 34% respectively believing he should step aside for his eldest son, currently the Duke of Cambridge.
The poll came as an unnamed minister and senior civil servant both expressed concern to the Independent newspaper about the prospect of Prince Charles intervening on political matters when he ascends to the throne.
Similar reports have been made in the past, notably in the diaries of Alistair Campbell, Downing Street director of communications under Tony Blair.
The minister told the Independent: "He has not caught up with the modern constitutional settlement... he wants to talk things through in very great detail on the issues he cares about.
"He gets upset if you turn up two minutes late for a meeting."
In Mr Campbell's diary entry for 31 October, 1999, published in July 2011, he recorded a meeting between Mr Blair and Charles shortly after he took Prince William fox-hunting in what was widely seen as a public challenge to the proposed ban.
ComRes said the last time it polled on support for the Prince of Wales becoming King ahead of his son, 41% agreed, while 42% said he should make way for William and 18% said they did not know.
The new poll involved interviews with 1,001 adults between 25 and 28 May.