Britain is due leave the European Union on 29 March, but Prime Minister Theresa May is struggling to get her exit deal approved by parliament, opening up huge uncertainty over whether a deal is possible, or even whether the country will leave at all.
May said the vote in parliament would be around 15 January, as expected, contrary to reports she could delay it.
Following the cancelled vote, May survived a leadership challenge triggered by disgruntled Eurosceptics in her party and has been back to Brussels to try and get additional reassurances about the so-called Irish backstop which was a major sticking point in opposition to the deal.
The Irish Examiner reported that a Democratic Unionist Party deputy leader has called on Prime Minister Theresa May to stand firm in requiring that the European Union changes its "poison" backstop provision on Northern Ireland's post-Brexit border.
As the parliamentary debate on her deal is due to begin next week, on 9 January.
Asked if he could guarantee that no one would die as a result of a no-deal Brexit, Mr Hancock told Sky News' Sophy Ridge On Sunday: "I'm confident that we will have the unhindered supply of medicines so long as the plans that we have in place are properly enacted".
Under forceful questioning from the BBC, May said that there should not be a second referendum.
Mrs May also refused to rule out holding a series of votes on her Brexit deal in the Commons if MPs reject it the first time around.
Labour's now policy is to push for another general election if Mrs May fails to get her Brexit deal through Parliament at a crucial vote scheduled to take place next week.
"Others across the House of Commons are so focused on their particular vision of Brexit that they risk making a flawless ideal the enemy of a good deal".
She did not answer whether she would, if defeated, make a second attempt to get the deal passed by parliament.
The YouGov poll of more than 25,000 people indicated a second referendum is backed by 75% of Labour voters.
"Given that parliament voted overwhelmingly, in the end, to have the referendum, parliament voted overwhelmingly, in the end, to accept the result of the referendum, and parliament has now legislated to implement the referendum, I find it rather lame that people are now saying "Oh, we didn't mean that".
Sir Vince Cable said: 'The time has now come for MPs to assert their authority by making it impossible for the government to collect crucial taxes if they do pursue a damaging no deal'.
Ms Thornberry said she believed another general election was the most likely way of breaking the current impasse on Brexit, adding that it could happen "within months".
"I don't think anybody can say exactly what will happen in terms of the reaction we'll see in parliament". The EU has shown in the past that it will move but only if faced with a resolute red line on the part of the UK Government.
"I don't agree with everything in the deal, I wanted to remain", he said.