Theresa May is seeking Conservative MPs' backing for the cabinet's proposal for UK-EU relations after Brexit.
The plan was agreed by the prime minister's senior ministers at a 12-hour cabinet awayday on Friday.
Mrs May said the plan "will be good for the UK and good for the EU".
But there has been unhappiness among Tory Brexiteers, with Jacob Rees-Mogg telling the BBC that when the detail emerged, it could yet be worse than leaving the EU without a deal.
Mr Rees-Mogg, leader of the European Research Group of Tory MPs, said that so far only the three page summary of the deal had been published, and he would have to wait and see the full 100-plus page document to see whether it was in line with the Conservative election manifesto, or amounted to a "punishment Brexit".
Labour leader Jeremy Corbyn said he was "not convinced" by the deal, and criticised "leaving out services from trade arrangements in the future... I've got a feeling the whole thing might start to unravel in the next few days".
All Conservative backbench MPs were invited to a briefing with the party's chief whip Julian Smith in Downing Street on Saturday, with about 40 thought to have attended.
The message from those leaving the briefing, such as Tory MP Nigel Evans, was that the proposal was for a "pragmatic" Brexit delivering on the big referendum issues of sovereignty, immigration and the national finances without harming the ability to trade quickly and freely with the EU.
Mr Evans said Mrs May would make a statement to Parliament about the plan on Monday and also address a meeting of all Conservative backbench MPs.
The plan that ministers signed up to on Friday aims to create a free trade area for industrial and agricultural goods with the bloc, based on a "common rule book".
It also supports what could amount to a "combined customs territory" for the UK and EU.
BBC political editor Laura Kuenssberg said the prime minister had "picked a side" by opting for a closer relationship with the EU than many colleagues desired - and she now had to sell it to her party and the other European leaders.
No 10, she added, hoped the new commitments would unlock the next phase of talks with the rest of the EU but it was not yet clear how many, or what kind, of objections had been raised within the cabinet.
Downing Street said the proposals marked a "substantial evolution" in the UK's position and would resolve outstanding concerns about the future of the border between Northern Ireland and the Irish Republic.
"This is a proposal that I believe will be good for the UK and good for the EU, and I look forward to it being received positively," Mrs May told the BBC.
One pro-Brexit cabinet minister told the BBC there was "no point" pushing for a vote as "we were well and truly outnumbered by 20 to seven".
The UK said it now wanted to accelerate the negotiations in an effort to secure an agreement by October, but also warned it will step up preparations for leaving on 29 March 2019 without a deal.
EU negotiator Michel Barnier, who earlier suggested the EU would be willing to shift its position if the UK relaxed some of its "red lines", tweeted to say the plans would be assessed to see if they were "workable and realistic".
#Chequers discussion on future to be welcomed. I look forward to White Paper. We will assess proposals to see if they are workable & realistic in view of #EUCO guidelines. Next negotiations w/ #UK on WP, & Withdrawal Agreement, w/c 16 July #Brexit— Michel Barnier (@MichelBarnier) July 6, 2018
What was agreed at cabinet meeting
The prime minister had gathered her 26 cabinet ministers together at her country residence to try to resolve differences over the shape of the UK's relations with the EU and break the current deadlock with the EU.
The main details of the Chequers statement are as follows:
- The UK would accept continuing "harmonisation" with EU rules on the trade in goods, covering only those necessary to ensure frictionless trade
- Parliament would have the final say over how these rules are incorporated into UK law, retaining the right to refuse to do so
- There will be different arrangements for trade in services, including financial products, with greater "regulatory flexibility" and "strong reciprocal arrangements"
- Freedom of movement as it stands will come to an end but a "mobility framework" will ensure UK and EU citizens can continue to travel to each other's territories and apply for study and work
- A new customs arrangement will be phased in, with the goal of "a combined customs territory"
- The UK will be able to control its own tariffs and develop an independent trade policy
- The jurisdiction of the European Court of Justice will end but the UK will pay regard to its decisions in areas where common rules are in force
Mrs May said this was an "important step" in the process of negotiating the UK's smooth exit from the EU.
"Of course we still have work to do with the EU in ensuring that we get to that end point in October. But this is good we have come today, following our detailed discussions, to a positive future for the UK," she said.
She said the proposals, to be formally published in a white paper next week, would give the UK the freedom to strike trade deals with other countries while maintaining regulatory, environmental and consumer standards.
In a letter sent to all Conservative MPs, she said she had allowed colleagues to express their views while policy was developed but "agreement on this proposal marks the point where this is no longer the case and collective responsibility is fully restored".
There is no mention in the document of either the single market or the customs union, which the UK has committed to leave after the end of a transition period in December 2020.
Under plans for a free trade zone, the UK would be committed legally to following EU law for a large part of the economy, including manufacturing and farming.
While Parliament would retain the right to diverge from EU regulations in these areas, the document makes clear that "choosing not to pass the relevant legislation would have consequences for market access, security co-operation or the frictionless border".
The document also commits the government to step up preparedness for a no-deal scenario, as one of a range of possible outcomes, "given the short period remaining before the necessary conclusion of negotiations".
Reaction to the deal
The CBI employers group welcomed the proposals for a free trade area in goods which it said would provide a "confidence boost" to business.
The Federation of Small Businesses said it was "encouraging" to see an agreed negotiating position from government.
But FSB chairman Mike Cherry warned: "The reaction from the rest of the EU is crucial for there to be concrete progress when negotiations restart in just over a week's time. The clock is ticking."
Shadow international trade secretary Barry Gardiner said there was "a danger that this is a lowest common denominator plan" designed to hold the cabinet together, rather than "secure the strong negotiating position that we need with the EU".
He told BBC Radio 4's Today programme: "Once upon a time we were told 'Brexit means Brexit', now we are told it means maintaining a common rulebook for all goods, a joint institutional framework for interpreting the agreement and the UK and EU forming this combined customs territory.
"That looks very much like regulatory alignment, the ECJ (European Court of Justice) and half a customs union to me."
Scotland first minister Nicola Sturgeon said the agreement was "hopefully a step forward".
But the SNP's leader at Westminster, Ian Blackford, called the agreement "a fudge", adding: "There might be agreement, for now, in the cabinet. The EU will not buy this."
Nigel Dodds, for the Democratic Unionist Party, said: "The government's commitment at Chequers to the political and constitutional integrity of the United Kingdom with no borders between Northern Ireland and the rest of the United Kingdom is a welcome reaffirmation of what is an absolute priority for us."
Sir Vince Cable, leader of the Liberal Democrats, said it could be the case that "Brexiteers have signed up to it knowing perfectly well that it is not going to pass the European Union and they'll then be able to blame Europe for the fact that it won't work".
Plaid Cymru MP Jonathan Edwards said: "This latest proposal continues to cherry pick certain aspects of EU membership in a way that the EU's negotiators have made perfectly clear is unacceptable. More fudge means yet more uncertainty and yet more damage to our economy."
Mixed views from Brexiteers
Transport Secretary Chris Grayling, who backed Brexit in the referendum, said the deal would end free movement of people and would end the remit of the European Court of Justice in the UK - saying that UK judges always pay regards to other countries' courts, such as Canada or Hong Kong.
He added, on BBC Radio 4's Today programme, that the cabinet had agreed to step up preparations for the UK leaving the EU without a Brexit deal.
Fellow cabinet Brexiteer Andrea Leadsom also tweeted her backing for the deal.
As a passionate Brexiteer with huge optimism about future as a free trading nation, I agree with the PM that keeping the UK together is vital. Alignment on goods, with Parliament sovereign on each decision, free to trade, no more vast payments, ending free movement - good for UK https://t.co/9ZKQkxSaXc— Andrea Leadsom MP (@andrealeadsom) July 7, 2018
Pro-Brexit campaign group Leave Means Leave said it would represent a "bad deal for the UK" which would "only slide further as the EU takes more and more".
Former UKIP leader Nigel Farage said the plan amounted to a "sell-out to global corporates" and would do nothing for the 90% of British firms which do not export to Europe.
Veteran Eurosceptic Tory MP Sir Bill Cash said he was "deeply disappointed to say the least" about the plans, which he suggested could contradict the terms of the EU Withdrawal Act passed by MPs last month.