A new pro-EU campaign group has called for Britain to retain its membership of the single market as it lays out its "ambitious" demands for a post-Brexit UK.
Open Britain has suggested that some curbs on the free movement of people could be negotiated, such as only allowing those with job offers to move to Britain.
But the group, which has taken over from the official Remain campaign Stronger In, says the UK should "mend not end" free movement and that any curbs must be part of a Europe-wide discussion on the future of the system amid mounting criticism.
The report, Stronger With Europe, is the first attempt by the group to sketch out what policies Britain should adopt as it negotiates its exit from the EU.
It comes just days after Prime Minister Theresa May held a Cabinet meeting at Chequers where it was stressed that any Brexit deal must include controls on the number of immigrants coming to Britain.
Highlighting a series of policy areas it is urging the Government to consider, the group stresses that protecting the UK economy must be a top priority and will launch a campaign to highlight the benefits of the single market.
The group, led by former ministers Anna Soubry, Pat McFadden and Norman Lamb, says the UK should be a member of the single market and negotiate a "bespoke UK-EU agreement which prioritises continued elimination of non-tariff barriers and continued influence over regulatory decision-making".
It says the UK should mitigate any negative consequences of free movement by introducing a Migration Impact Fund and a ban on agencies advertising solely overseas, and that it should guarantee the rights of existing EU citizens in the UK and UK citizens in the EU.
But its report does consider limits that could be placed on immigration, and says one option is "to examine tying the free movement of labour to offers of employment".
Former Conservative business minister Ms Soubry said: "Getting the best deal for Britain means starting the negotiations with ambitious goals. Britain is an ambitious country and we cannot succeed if we do not start with high ambitions.
"The campaign will marry a commitment to Britain's membership of the single market with making a positive case about the benefits of immigration. The present system needs further reform. It's particularly important people know the facts about immigration, we tackle their concerns and ensure the system works fairly for everyone."
The group is also calling for "deep co-operation" in security matters to continue, and for all EU funding to UK regions, universities, businesses, farmers and infrastructure projects to be protected until 2020.
They also stressed that Britain's commitment to tackling climate change must continue, and that all workers' rights guaranteed by the EU must be immediately translated into UK law.
Mr McFadden, the former Labour business minister, said: "The referendum decided that the UK would leave the European Union but it still left big, open questions about our future relationship with the EU and the rest of the world.
"These issues could have a major impact on jobs, investment, trade and employment rights in the future.
"Open Britain will not just argue for the best deal with Europe but for a more fundamental reform of our economy to make it work for the many, not just the few.
"We do not believe that people rejected the global economy at the referendum; we believe that their vote was a call to share more equally in it."
Mr Lamb, the former Liberal Democrat health minister, said: "The campaign has started the ball rolling in this debate, which will have many twists and turns.
"But it is vital that those who share our values speak up and do not cede the field to others outside of the centre-ground to dominate the argument."
The group has not called for a second referendum and says that "we respect the vote and are now campaigning for the best deal for all".
The report comes after Tony Blair suggested Britain could still stay in the EU if public opinion shifts away from Brexit over the next few years.
The former prime minister said the British people "have the right" to change their minds on the result of the June referendum.
Asked whether it was possible that opinion would move sufficiently to avoid Brexit, Mr Blair - speaking in French - responded: "At the moment, today, it is not probable, but the debate continues and I believe it is possible."
A Government spokesman said: "Brexit means Brexit and we are going to make a success of it. The Government will work hard to get the best deal for Britain."