The report, published last week by Migration Advisory Committee (MAC), suggested that British growers should be able to recruit a sufficient number of seasonal workers in the first couple of years after SAWS ends this year.
However, it warned that a replacement to SAWS is needed for the long term when growers will start facing recruitment problems.
MAC chairman Professor David Metcalf CBE said: "The current scheme is well managed and benefits UK growers, migrant workers and consumers in the UK, while not putting British workers at a disadvantage.
"It is well regulated and keeps long-term migration down due to the high return rate of workers to their home country.
"If growers cannot get the required labour, evidence suggests that a replacement SAWS would help horticulture thrive in the long run, but it is ultimately for the government to decide if this sector is a priority."
Anthony Snell, vice-chairman of the NFU's horticulture and potatoes board and the 2013 Soft Fruit Grower of the Year, said: "British growers have come to rely on migrant seasonal workers to produce and harvest their crops, so it is vital that we have access to a new SAWS after 2013, particularly given a rising demand for world-class British produce."
He said: "What's important now is that the Home Office makes a decision based on the evidence provided."
William Aveling, an asparagus grower based in Cambridgeshire, described the committee's recommendations as "very good news for the industry".
He added: "Many horticulture firms would go out of business if they did not have SAWS. It's not as though we can use English people to do all of our seasonal work. We have tried this and it just doesn't work - mainly because it is difficult for people to just stop what they are doing to work for an eight-week harvesting period.
"It's also hard, gruelling work. But the people we employ through SAWS are young and willing to work hard because they are primarily motivated by the money they can earn over here in the UK.
"They are paid by piece rate - so the more asparagus they cut, the more they can earn. They can earn as much as £10 an hour - there are not many jobs available to them that pay that much. So they get down to it."
Top fruit grower Paul Ward of Kent-based Mole End Farm said: "The findings of the report are completely and utterly correct. SAWS migrant workers contribute to the economy through National Insurance contributions and they work hard. If you take away that scheme, how are you going to fill the labour gap?"
The end of SAWS
SAWS allows an annual quota of 21,250 Bulgarian and Romanian workers to enter the UK for a maximum period of six months and accounts for one-third of Britain's seasonal agricultural labour.
It will close at the end of this year (2013) when A2 nationals gain free access to the European labour market and the UK transitional controls on these Eastern European nationals are lifted.