The European Council president said Tuesday that the bloc's "hearts are still open" to the United Kingdom if it changes its mind about Brexit.
Overall, 42% of people questioned for the research backed a second referendum in a "no deal" scenario, 32% opposed a second vote and 26% said they did not know.
In his speech, Tusk said Brexit is set to become a reality "unless there is a change of heart among our British friends".
Quoting the Brexit Secretary, he added: "Wasn't it David Davis himself who said "if a democracy can not change its mind, it ceases to be a democracy"?"
Sir Keir's comments also come as a new poll shows an increasing majority of the British public would back a second referendum should the prospect of leaving the European Union without a deal arise.
Meanwhile, during the same debate, the European Parliament's chief Brexit negotiator Guy Verhofstadt ridiculed Mr Farage's sudden interest in a second referendum, mockingly asking his adversary if Mr Juncker had "put something in his coffee or tea" to instigate the change of mind.
In a statement after the debate, European Parliament officials said: "MEPs cautioned the United Kingdom government not to take a Brexit transition deal for granted, and highlighted the need to formalise the withdrawal agreement as fast as possible".
Updating the European Parliament on a summit he chaired last month at which EU leaders agreed to open talks with London on their post-Brexit future, European Council President Donald Tusk took the opportunity to support those calling for a rethink.
Hammond told German weekly Welt am Sonntag in an interview published Saturday that those hoping London might do a U-turn on Brexit should "stop harking on about this illusion".
He insisted, however, it was still not too late for the British to have a change of heart and reverse its decision taken after a referendum in 2016 to remain within the European family.
German MEP Hans-Olaf Henkel attempted to bend Mr Juncker's ear and convince him to offer Britain a new European Union membership deal that hands more sovereignty to the United Kingdom parliament. Although the focus has so far been on the impact for the United Kingdom, the report shows the risks for both parties in the event Britain falls back to trading on World Trade Organisation rules, which would lead to greater costs from trade tariffs and the slower movement of goods across borders. The Commission is negotiating UK's departure from the EU.