Almost three quarters of people interviewed for a BBC Newsnight Opinion Poll think that there should be a general election soon after Tony Blair steps down.
73% of those asked favour an election after the new leader takes over the role.
The poll was carried out just ahead of the 10th anniversary of the election which brought Tony Blair to power.
Even a majority of those who describe themselves as Labour voters think there should be a general election - 52%, versus 44% who think there should not be.
Only 23% of the total polled thought there was no need for an early general election.
The trust issue
The poll also suggests that opinion of Tony Blair has gone down over the last five years.
A little over a quarter think the prime minister is trustworthy. When asked the same question five years ago almost half of those polled thought he was.
And just 34% think the prime minister is in touch with ordinary people - compared to 43% five years ago.
People also think the prime minister's international standing has gone down. Five years ago two thirds thought he was respected around the world - now less than half (45%) think that.
The polling was carried out by Communicate Research on behalf of BBC Newsnight.
They telephoned 1001 GB adults between 27th and 29th April 2007. Data were weighted to be demographically representative of all adults. CommunicateResearch is a member of the British Polling Council and abides by its rules. The same questions about the Prime Minister were asked by ICM on behalf of the BBC five years ago and then every year since except 2005.