The prime minister cancelled his talks with Kyriakos Mitsotakis in a row over the Elgin Marbles.
Viewers were left rather confused when the regular broadcast was interrupted.
The home secretary said the policy is deterring migrants from getting on small boats even though it hasn't begun yet.
John Kay made the quip as he grilled new Tory chairman Richard Holden.
The clip of the collision was featured on BBC Breakfast, causing Naga to break down with laughter.
Minister Laura Trott just called on viewers to judge the Tories on their "track record".
"They're not really comparable figures, are they?" Sally Nugent noted.
The health secretary seemed to deny much involvement in the Bibby Stockholm incident.
BRB, we’re retraining as meteorologists.
About BBC Breakfast
'BBC Breakfast' is corporation's early morning news and current affairs programme that airs daily from 6am on BBC One and BBC News, broadcast live from Salford Quays in Manchester. It is currently hosted by a team of presenters including Louise Minchin, Dan Walker, Charlie Stayt and Naga Munchetty, as well as stand-in hosts Mike Bushell and Steph McGovern. Carol Kirkwood acts as the show's resident weather presenter, hosting her segments from BBC Broadcasting House in London. Many of journalism's biggest names have presented the show over the years, including Bill Turnbull, Susanna Reid, Natasha Kaplinsky, Sophie Raworth, Dermot Murnaghan and Sian Williams. The show attracts an average daily audience of 1.5m, which is around double that of ITV rival 'Good Morning Britain', which is fronted by 'Breakfast' alumni Susanna Reid, along with Piers Morgan and Ben Shephard.