According to the results of the poll, almost 45 per cent of the respondents said that the lawmakers should not support the Brexit deal, and another 27 per cent could not give a definite answer. Additionally, over 33 per cent of the UK citizens believe that not only should the parliament vote the proposal down, but another referendum should be held on the country's membership in the bloc.
Another 27 per cent of the UK citizens would prefer the lawmakers to reject the deal as well and would choose to leave the bloc with no "divorce" agreement at all.
While almost 31 per cent of the respondents said that the deal with Brussels was bad, but London should nonetheless try and renegotiate its conditions, another 23 per cent believe that the country should leave with no deal. Only 12 per cent of the respondents said that the UK government should go for the agreement despite the fact that it was not good enough.
The poll also revealed that over 52 per cent of the respondents said that avoiding a hard Irish border was worth temporarily staying in the bloc's Customs Union.
More than 45 per cent of the respondents believe that it's not the right time to challenge the leadership of Prime Minister Theresa May.
The poll was conducted among a total of 505 respondents online on Wednesday, just hours after the UK Cabinet backed the draft EU-UK agreement, which had been confirmed on Tuesday. President of the European Council Donald Tusk said earlier on Thursday that the council would hold a meeting to finalize the agreement on November 25.
Over Half of Britons Want to Remain in EU After Draft Brexit Deal
In addition, a new poll by the Sky Data poll, published later in the day, showed that over a half of Britons wanted the United Kingdom to stay in the European Union and would back a second Brexit referendum. It was conducted among the channel's 1,488 clients and revealed that 54 per cent did not want Brexit, while 32 per cent would prefer a no-deal withdrawal. Only 14 per cent backed the draft.
Fifty-five per cent said they should have a second vote on whether to stay in the union. Slightly over 30 per cent also said Prime Minister Theresa May was the best person to lead the country through Brexit, while opposition Labour leader Jeremy Corbyn was backed by 24 per cent.
The deal has already prompted the resignation of UK Brexit Secretary Dominic Raab, Secretary of State for Work and Pensions Esther McVey and Minister of State for Northern Ireland Shailesh Vara.
The United Kingdom voted in favour of Brexit in 2016 and is set to depart from the European Union by late March 2019.