The pound skidded on Friday after the EU's chief Brexit negotiator Michel Barnier warned a transition deal was far from assured.
If in 2019, Rees-Mogg said, "The UK is subject to the European Court of Justice, takes new rules relating to the single market and is paying into the European budget ... are we not a vassal state?"
Australian High Comissioner Alexander Downer said a trade deal between his country and the United Kingdom could bring huge benefits to both.
European Union migrants will also continue to be allowed to move to the UK.
Sterling slipped back towards a three-week low against the dollar on Monday, weighed down by uncertainty among investors over whether Britain would succeed in securing a post-Brexit transition period.
The pound fell sharply against the dollar and the euro during Mr Barnier's speech before recovering slightly to stand about 0.7% down on the day.
NFU director of European Union exit and worldwide trade Nick Von Westenholtz said: "This statement is a strong signal urging Government to recognise the crucial role the food supply sector will continue to play in post-Brexit Britain". "If I have to be honest, I am surprised by these disagreements".
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There is "little prospect of companies getting comfort on the future trade agreement any time soon", he said.
"There was a very strong sense of denial among the people I saw, it really struck me", he added.
"We see fluctuations between countries and sectors but on the whole this is a surprisingly upbeat response", said John Maloney, head of FTI Consulting's Brexit taskforce.
Theresa May has been keeping the government's position deliberately vague as her ministers struggle to agree among themselves on exactly how they see Britain's future ties with the EU.
Michael Hewson, analyst at CMC Markets, said inflation data due on Tuesday would be important in determining sterling's direction, and that wages numbers due next week would be even more crucial as they would help shape the market's expectations for when and how fast the BoE would raise interest rates. However, Brussels said last week a transition deal was not a certainty and that London needed to clarify what it wanted from the EU.
"It's worked for us with 26 consecutive years of economic growth, partially because we've opened our market to the world", he added.
The issue of the border between Northern Ireland and the Republic of Ireland has also reappeared as a problem in the negotiations for the transitional period.