Recovering somewhat, Toner told the press, "I mean, look, we're always going to be able to work with the British, no matter who is occupying the role of foreign secretary, because of our deep abiding special relationship with the United Kingdom", reported BuzzFeed.
Davis, another leading Vote Leave campaigner, will be the new secretary of state for exiting the European Union.
The former mayor of London is no stranger to controversies, and his gaffes have made headlines around the world, including an incident in 2015, where he reportedly knocked down a 10-year-old child while playing touch rugby. At least one of his supporters has pointed out that as London's figurehead, he travelled the world in search of inward investment into the British capital.
His predecessor in the job was Philip Hammond, who was named finance minister on Wednesday.
The Eurosceptic will head the new Brexit department.
He had also come out strongly in support of Andrea Leadsom, May's last remaining opponent to the post of Conservative party leader before she withdrew on Monday.
Boris Johnson succeeded Philip Hammond in the Foreign Office.
Michael Fallon is the cabinet's defence secretary and ex-Energy Secretary Amber Rudd has been appointed home secretary.
Owen Smith has set out his stall for the Labour leadership by saying he would offer the public a second referendum to ratify any Brexit deal Britain strikes with the EU.
May, who had supported Britain's continued European Union membership, appointed leading "Leave" campaigner Johnson to a senior cabinet post while moving quickly to heal divisions sparked by the referendum.
Based in the UK, Larry is passionate about all things news and technology related. Mrs Cameron gave an emotional speech in which she said that "what people don't realise is just what happy times the last six years have been".
"That will be the mission of the government I lead".
Speculation had been rife over whether Mr Johnson would be given a role at all, given his spectacular and enforced retreat from the Tory leadership race, days after leading the Leave campaign to European Union referendum victory.
"The prime minister explained that we would need some time to prepare for these negotiations and spoke of her hope that these could be conducted in a constructive and positive spirit".
He urged his successor, "a brilliant negotiator", to "try to be as close to the European Union as we can be, for the benefits of trade, of co-operation and of security". I think she may be showing that she's out of her depth.
She will also attempt to unite a fractured nation in which many, on the evidence of the referendum, feel angry with the political elite and left behind by the forces of globalisation.
The veteran Tory, who has been a backbencher for almost 20 years, will be responsible for leading negotiations with Brussels over the terms of Britain's departure from the EU.
"The government I lead will be driven, not by the interests of the privileged few, but by yours".