And more Tory MPs believe the Prime Minister has handled talks on the UK's withdrawal from the European Union poorly (47 per cent) than well (34 per cent), according to the research.
The annual survey of MPs, conducted by The UK in a Changing Europe thinktank, and the Mile End Institute at Queen Mary University of London, suggested that the House of Commons has become more polarised in the last 12 months.
The survey also revealed that more than half (55 per cent) of Conservative MPs thought there were "alternative solutions" to the controversial backstop arrangement to prevent a hard border between Ireland and Northern Ireland, and that difficulties around the border question have been "exaggerated".
Meanwhile Leave MPs were highly sceptical about the likelihood of disruption in the even of no-deal - potentially posing a difficulty for Mrs May to use the potential risks to encourage them to support her deal, researchers said.
The survey showed that a majority of Mrs May's own MPs, in addition to an overwhelming majority in the Commons, think that she has handled the process of leaving the EU poorly.
Overall, 17 per cent of the Government approve of Mrs May's negotiations, compared to 70 per cent who disapprove.
But researchers said the survey showed "no obvious alternatives". "Our survey underlines the problems the PM would face in trying to garner a Commons majority for a softer Brexit than she has proposed," they wrote.
Opposition to membership of the single market has increased in the last 12 months, principally due to a movement away from this by Labour MPs.
Elsewhere, the figures revealed that 50 per cent of MPs and 80 per cent of Tory MPs feel customs union membership would not honour the result of the 2016 referendum.
In other words, this option would probably see Mrs May lose more Conservative votes than she gained Labour ones.
MPs were divided on whether a no-deal Brexit would lead to significant short-term disruption in Britain.
Leave MPs were highly sceptical about the likelihood of disruption, except in two areas: 44 per cent of Leave-voting MPs see a drop in the value of Sterling as likely (54 per cent unlikely), while 32 per cent see disruption at ports as likely (66 per cent unlikely).
Remain MPs saw both these eventualities as probable, 98 per cent anticipating a fall in the pound and 93 per cent expecting lorry queues.
Professor Anand Menon, director The UK in a Changing Europe, said: "The House of Commons is clearly very divided.
"It is hard to see, given the numbers, how the Prime Minister can get her deal through.
Countdown to Brexit: 79 days until Britain leaves the EU
"That being said, it is hard to see how any outcome can command a majority."
Professor Tim Bale added: "None of this will make easy reading for the PM: the attitudes of Leave-voting Tories appear to be hardening rather than softening and they seem amazingly unfazed by the difficulties presented by both the Irish border issue and a no-deal Brexit."
Interviews were conducted with 98 MPs, face-to-face, and findings are weighted to reflect the composition of the House of Commons.