MPs have told the watchdog reviewing their pay that they deserve a 32% hike to £86,250, leading to accusations they are living in "cloud cuckoo land".
A survey carried out by the Independent Parliamentary Standards Authority (Ipsa) also found more than a third believe they should keep generous final salary pensions.
The findings emerged as Ipsa published a report on its initial consultation into pay and pensions, which ended last month.
The research, which politicians completed anonymously, found that 69% thought they were underpaid on £65,738.
The average level suggested for the salary was £86,250.
Unison general secretary Dave Prentis said MPs should "get real": "At a time when millions of workers are getting zero pay rises, the idea that MPs believe they deserve a 32% increase is living in cloud cuckoo land.
MPs have told the watchdog reviewing their pay that they deserve a 32% hike to £86,250
"MPs should get real about pay, this shows they are totally out of touch with working people. How can they think that they deserve a 32% increase when the rest of the country is being told to tighten their belts?"
But Tory MP Andrew Bridgen told BBC Radio 4's PM programme he believed MPs deserved more cash.
"Most of my colleagues on the government benches took a large pay cut to be an MP, and I think there’s a real danger, if you need good people, you need the right people, there’s a lot of exclusion," he said.
"A man or a woman who’s very capable, doing very well in their profession, whatever that may be, with a family, are they going to be willing to take that pay cut, look their children in the eye when it’s Christmas say you can’t have what you normally have because Mummy or Daddy wants to be an MP."
Ipsa watchdog will put firm proposals out for consultation in the spring, with final decisions likely to be taken in the autumn.
YouGov conducted online interviews with 100 MPs on Ipsa's behalf, and weighted the results slightly to represent the Commons by party, gender, year elected, and geography.
Conservatives were the most likely to believe they were underpaid, with 47% saying that was the case. Some 39% of Labour members and 9% of Lib Dems held the same view.
On average, Tories said their salary should be £96,740, while Lib Dems thought the right amount was £78,361 and Labour £77,322. Other parties put the figure at £75,091.
One MP said they should be paid £40,000 or less. Some 5% said £60-65,000 was fair, and 17% went for £65-£70,000.
A fifth of those questioned said they should be paid £95,000 or more.
The research found that 27% of the MPs believed their pay should go up by more than 1% over the next two years - despite public sector rises and most working age benefits being controversially capped at that level.
However, nearly two-thirds said they should be subject to the same restraint.
Some 53% wanted to bring back so-called "golden goodbyes" worth tens of thousands of pounds that were previously handed to members who step down from parliament voluntarily.
Ipsa also confirmed that it is not proposing to introduce performance-related pay, regional pay or to take outside earnings into account.
Chairman Sir Ian Kennedy said: "In the past, MPs have agreed their pay and pensions among themselves. So this new approach of independent decision-making marks a real and important change and is another crucial step in helping Parliament to regain the trust of the public.
"The consultation we held over the autumn has been hugely informative and important in directing our thinking. It also serves to show the spread of views and depth of feeling on this issue.
"We remain committed to listening and I would urge people to get involved in this debate."
Asked what David Cameron thought of MPs' demand for more pay, the Prime Minister's official spokesman said: "The Prime Minister's view is that MPs' pay is a matter for Ipsa. The 'I' in Ipsa stands for 'independent'."
When asked whether the PM believed that MPs should be subject to the same pay restraint as public sector workers, the spokesman said: "The Government's position on public sector pay is well-known."