The handwritten notes, carried by an aide to Conservative party MP Mark Field, the vice-chairman of the party, included phrases like "what's the model? Have your cake and eat it" and "unlikely" in reference to the European Union single market.
"I was interested and amused to see it because it doesn't reflect any of the conversations that I've been part of in Downing Street," said UK business secretary Greg Clark, forced to react to the media storm around the notes.
Downing Street said the notes, captured on a long-lens camera by photographer Steve Back, were not written by a government official and do not reflect its official position.
"These individual notes do not belong to a government official or a special adviser. They do not reflect the government's position in relation to Brexit negotiations," a spokesperson for 10, Downing Street said.
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The document also says the triggering of Article 50, which formally starts Brexit negotiations, could be "difficult".
It reveals that the EU's chief negotiator, Michel Barnier, "wanted to see what the deal looks like first" but the government does not want to provide details.
It says Britain wanted to have a "Canada plus" trade deal rather than remaining a member of the European Economic Area (EEA) but negotiating over services, especially the financial sector, is likely to be "difficult".
A spokesperson for British Influence said, "It is likely there will be a legal action because, in our view, the government has taken a stance that leaving the EU means leaving the single market".
The latest memo, scribblings on an A4 sheet of paper, will come as an embarrassment for British Prime Minister Theresa May, who has repeatedly refused to give any details of her strategy, insisting she won't give a "running commentary" on the process of leaving the EU amid concerns that it would give away Britain's hand.
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