Almost 80% of people questioned in a telephone poll for the BBC have said Britain should retain its monarchy.
Nearly 70% said monarchy should not end with the present Queen
Some 78% of respondents agreed that Britain should still have a royal family and 19% disagreed.
Asked if the monarchy should end when Queen Elizabeth dies, 68% disagreed and 28% agreed.
The Gfk NOP survey of 1,000 people aged 16 and over was commissioned by historian Prof Peter Hennessy, guest editor of Radio 4's Today programme.
When asked if there will be a monarchy in 30 years' time, 80% said yes and 15% said no.
Meanwhile, a separate poll has suggested that most young people would keep the monarchy, despite more than half saying the royals do not provide value for money.
Nearly 70% of 18 to 24-year-olds would keep the royals and overall only 16% of people would vote for a republic.
The poll of 1,004 people, commissioned by Discovery Channel, found that over 80% thought that Prince William's girlfriend Kate Middleton would be a good addition to the Royal Family.
But William's stepmother Camilla received less support from the public - with less than half of those questioned saying she was a good ambassador for the Royal Family.
Almost 70% of people said they still had more admiration for Diana, Princess of Wales, than for Prince Charles's new wife.