"Talks between the European Union and Britain on Brexit are being conducted in a spirit of "good cooperation", Michel Barnier, the EU's chief negotiator on the issue, said on Monday".
And Number 10 posted a video lasting nearly seven minutes on social media in which the Prime Minister set out her plan.
International Trade Secretary Liam Fox - another top Leaver in the cabinet - said Brussels had made "reassuring noises" in recent weeks on the Brexit talks.
The alternative, May has said, is that Britain will leave without a deal on March 29 next year.
Negotiations are a critical stage, with both sides hoping for an agreement on the terms of the UK's withdrawal and future trade relations by the start of November at the latest.
The party's stance on Brexit is expected to be debated at the gathering and Mr Lammy said: "A People's Vote is not only the right thing to do for jobs, public services and the future of our young people - it's the best way to get a radical Labour government".
He added: "We're urging the Government to concentrate on getting a deal to ensure the continuation of tariff and friction free trade which is so important to the future of our economy".
The EU's backstop proposal has been rejected by the UK because it effectively creates a customs border in the Irish sea, while the UK's plan was rejected by the UK because it was temporary and applied to the whole of the UK, rather than only Northern Ireland.
UK leader warns rebels: It’s my Brexit agreement or no deal
The gloomy assessment contrasts with that of May, who indicated last week that a no-deal hard Brexit would not be a disaster for Britain.
He reiterated he was equally keen to prevent a hard border between Northern Ireland and Scotland as between Northern Ireland and the Republic.
She is hoping to make progress toward a deal when she meets fellow European Union leaders this week.
"There are still parts of the withdrawal agreement that require further negotiation".
"The ancestors of many people we represent fought alongside the British in two world wars, but are now forced to stand aside in favour of people with no connection to the United Kingdom".
Brussels' chief Brexit negotiator will brief ministers from European Union governments on the state of talks with the United Kingdom ahead of a major summit this week.
"And I think actually in reality if we got to the situation where we had a deal and it was voted down ... you would risk tripping up into the no-deal scenario because there would be such a tight timeframe".
The backing of Khan, a member of the main opposition Labour party, for a second referendum will put more pressure on Labour leader Jeremy Corbyn to change his opposition to the idea when the party meets for its annual conference in a week's time.
Ellvena Graham, chair of the Northern Ireland Chamber of Commerce, told Mr Donohoe the British government's Brexit guidance for businesses had "done nothing" to help them prepare and had only "confused them more".