The arrival of 1,085 people in only three days is particularly politically damaging because it came as Labour gathered in Liverpool for its annual conference. Immigration has become one of the most difficult issues for the new administration, with voters demanding visible evidence that ministers are capable of securing the border.
For Mr Burnham, the timing could hardly be worse. The Prime Minister has repeatedly insisted that tackling illegal migration is one of the Government’s priorities, while Home Secretary Shabana Mahmood has promised a tougher approach to people-smuggling gangs and the systems that allow migrants to remain in Britain.
Yet the sheer scale of Wednesday’s arrivals has given opposition parties an opportunity to argue that the Government’s promises are not translating into results.
The 781 arrivals recorded on September 23 represented the highest daily total so far this year. Combined with the 150 people who crossed on Monday and another 154 on Tuesday, the three-day figure exceeded 1,000.
Conservative MPs have seized on the numbers as evidence that ministers are losing control.
Shadow Home Secretary Chris Philp argued that the fact boats were able to cross the Channel without being intercepted raised serious questions about surveillance, cooperation with France and the effectiveness of the Government’s border strategy.
The Conservatives have also renewed calls for Britain to adopt a much more aggressive deportation policy. Their argument is that as long as migrants believe they have a realistic chance of remaining in the UK after making the crossing, criminal gangs will continue to market the journey as an attractive option.
The Government strongly disputes the idea that there is a single policy capable of instantly ending the crossings. Ministers point to the dangerous nature of the Channel, the sophistication of smuggling gangs and the constantly changing tactics used to launch boats from the French coastline.
But the political problem for Labour is that voters are unlikely to judge the policy primarily by the complexity of the challenge. They are likely to judge it by whether the number of boats is rising or falling.
That makes the latest figures particularly uncomfortable.
Mr Burnham has sought to emphasise that crossings are lower than at the same stage of previous years. He has also refused to give a specific deadline for ending the crossings, arguing that making a promise about an exact date would be irresponsible.
However, this approach leaves Labour vulnerable whenever a large number of boats arrive in a short period.
The Government can point to longer-term trends, but opposition parties can point to individual days and ask a much simpler question: if the policy is working, why are hundreds of people still arriving in a single day?
Another major issue is Britain’s relationship with France.
Mr Burnham has argued that Brexit reduced the level of cooperation that previously existed between Britain and European partners. He said the UK and the EU once had a more cooperative system for tackling cross-border problems, and that Britain can no longer rely on exactly the same arrangements.
That argument is likely to become increasingly controversial.
Brexit supporters reject the suggestion that leaving the European Union should be used to explain the persistence of Channel crossings. They argue that Britain remains capable of negotiating bilateral agreements with France and other European governments and should focus on securing practical arrangements rather than revisiting the referendum.
The dispute therefore goes beyond immigration policy. It has become another battleground over Brexit itself.
For Labour, there is also a growing danger that immigration will divide the party.
Some Labour MPs and trade union figures have called for a more humane approach to asylum seekers, while others believe the party must demonstrate that it can enforce immigration rules and restore confidence among voters who are worried about uncontrolled migration.
The Government is therefore attempting to balance two very different political pressures.
On one side are voters who want tougher border controls, faster removals and a reduction in the number of people arriving by boat. On the other are campaigners who argue that asylum seekers should not be treated as criminals simply because they entered Britain irregularly and that the country has international obligations toward people fleeing persecution.
The arrival of more than 1,000 people in three days brings those tensions into sharp focus.
There is also the question of accommodation. Every additional arrival places pressure on the asylum system, particularly when processing cases takes considerable time. The Government has promised to reduce its reliance on expensive asylum hotels, but large numbers of new arrivals make that objective more difficult.
Local communities have increasingly become part of the political debate. Where asylum seekers are housed can generate intense opposition, particularly in areas where residents believe they have not been adequately consulted.
Labour therefore faces a difficult political equation: it must demonstrate compassion while simultaneously convincing voters that the immigration system is controlled.
The Government has also promised to target the criminal organisations behind the crossings. Ministers argue that the people-smuggling networks are the real source of the problem and that dismantling those networks is more effective than simply intercepting individual boats.
That strategy, however, takes time.
Smuggling organisations can change launch locations, replace boats and adapt to enforcement measures. When French authorities increase patrols in one area, gangs can attempt to move operations elsewhere. The Channel itself also creates enormous logistical challenges for both governments.
Critics say that explanation risks becoming an excuse.
Supporters of the Government counter that no serious policy can guarantee that every boat will be stopped, particularly when smugglers deliberately put migrants into overcrowded and unseaworthy vessels.
There is another uncomfortable reality for ministers: every successful crossing can strengthen the perception that the route remains viable.
This is why the Government is under pressure to demonstrate not only that it can rescue people at sea, but that it can reduce the incentive for smugglers to launch boats in the first place.
The latest figures will therefore intensify scrutiny of the Government’s forthcoming immigration measures.
Mr Burnham has promised that he will not stop until the criminal networks responsible for the crossings have been tackled. The Home Secretary has made similar commitments.
The political test will be whether those promises eventually produce a sustained reduction in arrivals.
For now, the opposition has been handed a powerful line of attack. More than 1,000 people arriving in three days creates an image of a border under severe pressure, regardless of whether the annual total is ultimately lower than in previous years.
And that distinction could prove crucial.
Labour can argue that the long-term figures matter more than a single exceptional week. Conservatives and Reform UK can argue that each individual arrival represents another failure to prevent an illegal crossing.
The debate is unlikely to disappear soon.
Indeed, as the Government prepares to unveil further measures, the question hanging over Downing Street is becoming increasingly direct: can Mr Burnham turn promises of tougher enforcement into measurable results, or will the Channel crisis become the issue that defines his premiership?
For now, the Government insists it has a plan.
But after 1,085 arrivals in just three days, its opponents are demanding something more tangible than another promise. They want to see the boats stop.