The Prime Minister stopped short of announcing that Britain would seek to rejoin the EU, the single market or the customs union. But his language marked a significant shift in tone and immediately raised questions about whether Labour could eventually campaign for a much closer relationship with Brussels.
For Brexiteers, the remarks will be viewed as a warning that the question they believed had been settled by the 2016 referendum could once again become a central political battleground.
For Labour supporters who opposed Brexit, however, Burnham’s intervention is likely to be welcomed as an acknowledgement that the current relationship with Europe is not delivering the economic and political benefits that were promised.
The Prime Minister argued that Brexit had failed to provide the greater control that voters were promised.
Instead, he claimed, Britain had lost some control over important areas including the economy and immigration.
That argument strikes directly at one of the central claims made by Leave campaigners during the referendum: that leaving the EU would allow Britain to take back control of its laws, borders and economic policy.
Burnham now appears to be challenging the idea that sovereignty alone has delivered better outcomes.
His intervention is particularly significant because he has not simply called for closer cooperation with Europe. He has suggested that Britain must consider its long-term relationship with what remains its largest market.
The timing is also important.
A UK-EU summit is expected to provide an opportunity for both sides to discuss issues including trade, security and migration. Burnham has suggested that Britain needs to go beyond individual agreements and consider the broader strategic relationship.
That could eventually include discussions about regulatory alignment, trade barriers and closer cooperation on migration.
But the Prime Minister faces a difficult balancing act.
The Labour Party must appeal to voters who remain uncomfortable with Brexit while avoiding the impression that it is attempting to overturn the referendum result without a clear democratic mandate.
This is why Burnham’s decision to talk about “different options” rather than immediately announcing a return to the EU is politically significant.
It allows him to open the debate without committing the Government to one particular destination.
The Prime Minister can argue that he is simply being realistic about Britain’s economic interests.
Critics, however, are unlikely to accept that explanation.
Brexit supporters will argue that voters already made their decision and that politicians should concentrate on making Brexit work rather than reopening the question of membership.
They will also point to the fact that leaving the EU gave Britain the ability to negotiate its own trade agreements and establish policies independently of Brussels.
The Government will therefore face questions about exactly what it believes went wrong.
If Brexit has “done more harm than good”, what specifically does Burnham want to change?
Would Labour seek a closer customs arrangement?
Would it support greater alignment with EU regulations?
Would it consider freedom of movement in some form?
Would Britain eventually seek membership of the single market?
And most controversially, would Labour eventually support rejoining the European Union itself?
None of those questions has been definitively answered.
That uncertainty may be deliberate.
Burnham is likely to understand that the Brexit divide remains politically powerful. A direct pledge to rejoin the EU could provoke fierce opposition from Leave voters and provide Reform UK and the Conservatives with a straightforward campaign message.
Instead, the Prime Minister can argue that Britain should examine the evidence and choose whatever relationship best serves the national interest.
The economic argument will be particularly important.
Supporters of closer European integration argue that Brexit has increased friction for British exporters and importers. Businesses trading with European countries must navigate additional paperwork, rules and border procedures that did not exist when Britain was an EU member.
For companies that rely heavily on European supply chains, even relatively small barriers can increase costs.
Brexit supporters counter that Britain now has greater freedom to develop its own economic policies and sign agreements with countries outside Europe.
The United Kingdom has already pursued trade relationships beyond the EU, and proponents argue that Britain should use its independence rather than attempt to recreate membership through a series of closer agreements.
The argument over immigration is even more complicated.
One of the strongest reasons many voters supported Brexit was the promise of greater control over immigration.
Yet Burnham argues that Britain has not achieved the level of control that voters were promised.
His comments suggest that the Government may be looking for a new migration arrangement with European countries.
That could involve greater cooperation over border enforcement, returns agreements and the movement of workers.
But there is an obvious political tension.
Closer cooperation with the EU could help Britain tackle some migration challenges, but any arrangement involving greater movement of people could immediately become controversial among voters who supported Brexit specifically because they wanted tighter immigration controls.
Burnham therefore needs to demonstrate that a closer relationship with Europe does not automatically mean returning to the pre-Brexit system.
His broader political programme adds another layer to the debate.
The Prime Minister has already promised major reforms including a National Care Service, changes to public ownership, housing reforms and electoral reform.
His announcement on Brexit therefore forms part of a much wider attempt to present Labour as a party willing to reverse what he describes as decades of economic and political mistakes.
Burnham attacked deindustrialisation, deregulation, privatisation, austerity and Brexit as part of what he described as Britain being on the “wrong path”.
That is a deliberately broad political argument.
Rather than treating Brexit as an isolated question, he is placing it inside a larger narrative about how Britain should be governed.
The message is that the state should take a more active role in the economy, public services and strategic industries, while rebuilding closer relationships with European neighbours.
For supporters, this represents a decisive break from the policies that dominated British politics for decades.
For opponents, it risks creating an expensive expansion of government while reopening arguments that Britain has already spent years trying to settle.
The reaction from Reform UK is likely to be particularly aggressive.
Nigel Farage and his colleagues have made defending Brexit central to their political identity. Any suggestion that Britain should move towards rejoining the EU gives Reform an opportunity to present itself as the strongest defender of the referendum result.
The Conservatives will face a similar dilemma.
They will have to decide whether to defend Brexit as a matter of principle or focus on the practical consequences of any proposed changes.
Labour, meanwhile, will have to manage divisions within its own ranks.
Some Labour MPs and activists strongly support closer European integration, while others will be wary of reopening the issue and alienating voters in constituencies that backed Leave.
That makes the next stage of the debate particularly important.
Burnham has promised to explain the different options surrounding Britain’s future relationship with the EU.
When he does so, voters will be looking for specifics rather than slogans.
If the Government believes Brexit has caused economic damage, it will need to identify the problems clearly and demonstrate how closer European cooperation would solve them.
If it believes immigration controls could be improved through greater cooperation with Brussels, it will need to explain how that can happen without recreating the freedom of movement system.
And if rejoining the EU is genuinely under consideration, the public will eventually demand to know what price Britain would have to pay.
For now, Burnham has deliberately left the door open.
That may be the politically safest position, but it also guarantees that speculation will continue.
The two words “more harm than good” could become some of the most important words of his premiership.
They represent a fundamental judgement on one of the biggest political decisions of modern British history.
The question now is whether Burnham intends merely to improve the relationship with Europe or ultimately to begin the journey towards reversing Brexit altogether.
For millions of voters, that distinction will matter enormously.