The report, published by the British Foreign Policy Group, an independent think tank advocating for a stronger UK global presence, shows that under a quarter of those surveyed believe the Prime Minister's deal is "the best framework for our relationship with the EU moving forward."
The question of what it should be replaced with, however, reveals that nearly five years since the UK decided to leave the European Union, the nation is still bitterly divided on what role Britain should have in Europe.
While 27% of respondents wanted a much closer relationship with a view to rejoining and 22% want a closer relationship but to remain outside the bloc, 12% want to move further away from Europe. Of the 24% of respondents who approved of the deal, they did so with an important caveat that it was the best deal for the "foreseeable future". Some 15% of respondents said they didn't know.
The survey, conducted in the week after the deal came into effect on January 1, is the first major temperature check on what Brits think of the reality of Brexit. Even though the UK formally left the EU on March 31 last year, transition arrangements ensured that little of consequence changed until the end of December.
But since then, trade between Great Britain and Northern Ireland has been disrupted, the UK's financial markets have lost business to continental Europe and British exporters have been forced to watch fresh produce rot as new trade barriers prevented exports reaching European markets in time.
British sentiment towards Europe remains difficult to unpick. Broadly, attitudes have softened in the past 12 months. While only a minority wish to rejoin the bloc, a majority of respondents said they viewed the European Union as a more important international partner for the UK than the United States.
And while many younger, metropolitan voters are more pro-European than older voters, the report notes that more than a quarter of respondents who voted to leave the EU describe themselves as "European."
The survey, which was conducted on behalf of BFPG by pollster Opinium, asked 2,002 British citizens questions ranging from what they thought of Johnson's Brexit deal to how much they really cared about the so-called "special relationship" with the United States.
Most respondents were broadly positive that the UK should be active on the world stage, largely in the areas that Johnson says are a priority for his government. Johnson has made clear that he wants to use his chairmanship of the G7 this year, as well as the UK's position as host to the United Nations Climate Change Conference, to make a statement about post-Brexit Britain's commitment to the international order.
Uncomfortably for Johnson, the report also reveals challenges for his "global Britain" agenda among British voters. The Prime Minister has long claimed that an advantage of Brexit would be the freedom to pursue independent foreign policies in trade, environmental issues, national security, normal leadership and foreign aid.
Indeed, a majority believe that UK spending on foreign policy should be maintained or increased, support a multilateral approach to climate change and would like to see Britain showing moral leadership.
But when it comes to international relations in the round, Johnson falls short of a ringing endorsement: 49% of respondents said they didn't trust the UK government on foreign policy, compared to 39% who did. Some 12% did not know. It might also alarm Johnson to find that the voters he prised away from other parties to deliver his victory in 2019 -- with his pledge to "get Brexit done" -- are the most isolationist.
"Our research makes clear that building public consent around the Global Britain project will be one of the central tests, and biggest challenges, that Boris Johnson will face in his premiership," said Sophia Gaston, director of the BFPG. "The Conservative Party's voter base is in a state of evolution, and is moving away from the Prime Minister's own instincts towards internationalism and openness. Meanwhile, many other voters are repelled by Global Britain's associations with Brexit."
However, she adds, "I'm optimistic that a once-in-a-generation project to bring the country together around a common vision for the UK's role in the world can succeed, but it will be a hard slog to realize this ambition."
The report, perhaps unsurprisingly, paints the picture of a nation coming to terms with the most significant shift in its domestic and foreign agenda for decades, unsure of what its next steps should be. And for many, it will confirm the view that the 2016 vote to leave the EU has created a new divide in British politics that is some way from being bridged.