In leaked emails seen by the Mail on Sunday, Dr Tim Leunig is understood to have said the food sector was "not critically important" to the country's economy - and that agriculture and fisheries "certainly isn't".
The economic adviser to the Chancellor was also reported to have said ministers could follow the example of Singapore which is "rich without having its own agricultural sector".
But National Farmers' Union (NFU) president Minette Batters rubbished such a comparison, telling Sky News' Sophy Ridge on Sunday: "Singapore has 5 million people, and doesn't have any farmed landscape so it actually has to import all its food.
"Here 75% of Britain is a farmed landscape, we have a fantastic maritime climate in which to produce our food, and we have 60 million-plus people here to feed so there's a sort of moral imperative, if you like, for us to be able to produce food in this country.
NFU Leader urges Government not to back down in trade talksYorkshire faces third weekend of flooding as Storm Jorge hits region"So absolutely we need our farmers and we're the bedrock of the largest manufacturing sector providing all those raw ingredients and currently at 60% self-sufficiency."
Ms Batters said Britain can be "global leaders" in climate-friendly farming, adding: "There's a real opportunity for this Government to lead based on standards, integrity, and actually putting farmers at the forefront of delivering on climate change.
"So we have to see this as an opportunity and comparisons with Singapore are just completely out of touch with where this country is."
The Government distanced itself from the comments made by the Treasury adviser although the published opinions are likely to propel industry fears that ministers could discard safeguards for farmers and fishermen in the forthcoming post-Brexit trade talks with the US and the European Union.
A spokesman said: "We have made clear the comments are not in line with Government policy."
Sources said the remarks were made in personal emails and that Dr Leunig was not speaking in his Treasury role.
The agriculture and fishing sectors represent fewer than 1% of the UK's economy respectively.
But rural and coastal communities voted 'out' in large numbers during the 2016 referendum after the Vote Leave campaign argued that farmers and fishermen would be better off once free of EU rules.
Food standards have proved to be a dominating issue as negotiators prepare for trade talks with their US counterparts in the coming weeks.
Last week, Environment Secretary George Eustice came in for criticism after he refused to rule out chlorinated chicken and hormone-treated beef being imported from the US as part of a trade agreement with Washington.
Allowing such treated and often cheaper foods into the UK could undermine British farmers who operate to higher standards.
Fishermen also fear promises made to them on increased catch quotas and controlling who fishes in British waters could be traded in exchange for market access during the talks with the EU, which are due to begin next week.
Brussels has made clear it wants little to change in terms of access for European boats and quota allocation once the transition period is over in December.
Dr Leunig's comments would not be the first time a Government figure has managed to upset UK industry.
Boris Johnson is said to have made controversial comments on the topic of Brexit, having reportedly said "f*** business" when questioned about the sector's concerns over a no-deal exit from the EU in 2018.
Treasury adviser and academic Dr Leunig is said to be close to Dominic Cummings, the Prime Minister's chief adviser in Downing Street.
Mr Cummings has called for "weirdos and misfits" to join the civil service in a bid to break the mould of current Whitehall thinking.