Farrer said he agreed with environmental campaigner George Monbiot, who has campaigned for rewilding the fells to prevent run-off.
Large areas of the Lake District flooded this month, many for the third time in 10 years, despite the Environment Agency spending millions on hard landscaping solutions such as walls.
The Farrer Huxley Associates landscape architect, who splits his time between his London office and Grange-over-Sands, said: "It is utterly clear what Monbiot is saying, which is in the Lake District sheep cause close-cropped grassland and tree-covered fells are 67 times more absorbent than that grassland, so water is going to run off that grassland 67 times more quickly."
He said although sheep farming is "in the blood" of Cumbrian people, the grassland that sheep produce is low in biodiversity and heavily subsidised.
Sheep farmers earn an average £15,000 a year and CAP and other subsidies keep the sector afloat, he added.
He said the landscape produced was "no more natural than a car park at the bottom of the fell".
Farrer suggested that managing woodland was "more viable than unviable sheep farming" and would save money long-term on dredging, flood clear-ups and flood mitigation.
He added that landscape is complex and "the idea of saying to Government dealing with sheep farming and Europe and CAP that this is what you need to solve flooding is impossible for the Government because the Government works in silos".
Farrer said in the same way that education money should be spent on school grounds, health money on greenspace and Home Office money on greening to make safer places, Government cash, not just from cash-strapped Defra, should go on re-wilding fells. He said areas such as Snowdonia, the source of flooding in Worcestershire and Gloucestershire, also needed a similar approach.
He said a combination of 'hard' solutions such as walls and green solutions was preferable as rewilding was a long-term way of fixing the problem and that Governments needed to think further ahead when making flood mitigation decisions.
Farrer said if the floods had come in London down the River Thames "then people would have started to join it up".