Harry hears Vernon calling for him. He takes his time putting down the mirror fragment and goes downstairs to find Vernon, Petunia, and Dudley all dressed for traveling. Vernon tells Harry he's decided he doesn't believe it and won't go. Harry rolls his eyes; Vernon has been changing his mind daily about whether or not to let wizards take him into hiding. Vernon recoils when Harry reminds him of Kingsley Shacklebolt and Mr. Weasley's visit a few weeks ago, when they explained that the Dursleys won't be safe here once Harry turns seventeen. Vernon asks why the Ministry can't protect them, but Harry reminds him that the Ministry is compromised.
At this point, Vernon is having to learn lessons that Harry learned several novels ago: that governments (and particularly, the Wizarding government) aren’t something that he can trust blindly. Vernon, like Voldemort, places more emphasis on the displays of power, which he equates with the establishment and not with fringe resistance groups like the Order of the Phoenix. Further, accepting that Harry is right about this will mean that Vernon has to walk back his critiques of the magical world—something that's certainly going to be uncomfortable for him.
Vernon asks why they can't have Kingsley protect them—Kingsley is better at dressing like a Muggle and has a reassuring voice. Harry reminds Vernon that Kingsley is protecting the Muggle Prime Minister and points out the "accidents" on TV are Voldemort, not accidents, and the fog is caused by dementors. Dudley looks terrified, but Vernon asks what they're supposed to do about work and school. Dudley says loudly that he's going with the Order. They'll arrive in a few minutes and Harry wonders what he should say after sixteen years of abuse.
Dudley's choice to go with the Order continues to build the case that Dudley isn't as unintelligent or as interested in pure brute strength as Harry thought he was. Though this choice is certainly motivated by fear, his willingness to accept as truth something that he also fears, but that he knows will save him, represents a major leap for Dudley and suggests that he might finally believe Harry.
Harry heads back upstairs to comfort Hedwig, but returns to the living room when he hears Dedalus Diggle and Hestia Jones arrive and greet the Dursleys. Dedalus explains the plan and politely asks Vernon if he can drive. Vernon is flabbergasted, especially when Dedalus's pocket watch screams at them to hurry up. Vernon makes to shake Harry's hand but can't bring himself to do it and then heads to the door with Petunia. Dudley, however, asks why Harry isn't coming with them, and where he's going to go. Everyone is shocked, and Hestia gets angry when Vernon says that Harry's going off with "their lot." Harry reassures her and says that the Dursleys think he's a waste of space, but Dudley says he doesn't think that about Harry since Harry saved his life.
Telling Harry that he's not a waste of space shows that, at least now, when he possibly won't have to see Harry again, Dudley is comfortable behaving in a kind and vulnerable way to Harry. This continues to show Harry that if he's willing to look, he'll be able to find allies in all manner of unexpected places—even in a place that he hates and has historically been abusive toward him. Dudley now, on some level, joins the people resisting Voldemort on Harry's behalf and the people who support Harry.
Harry stares at Dudley and realizes that Dudley may have left the cup of tea as an act of kindness, not a trap. Petunia bursts into tears and embraces Dudley, while Hestia and Dedalus try to move things along. Dudley pulls away from Petunia and shakes Harry's hand. They smile at each other and Dudley leaves. Harry and Petunia stare at each other for a moment and it seems as though she wants to say something, but she leaves without a word.
Being the only one willing to shake Harry's hand suggests that, in this moment, Dudley himself begins to come of age and differentiates himself from his cruel parents. He opens the door to have a relationship with Harry in the future, and the handshake offers Harry some small sense of support from this unexpected corner.