They believed it was a move that would provide important stability for British farm businesses.
The industry's welcome, which followed May's high-profile Brexit speech in Florence, stopped well short of any actual celebration of what she said, however.
That included the issues surrounding future UK trade deals, both with the EU and others, over which widespread confusion remained.
"More details are needed if farmers and growers are to have the certainty to plan and invest in their businesses in the future," National Farmers Union international trade adviser Gail Soutar said.
"Farmers and growers are becoming increasingly alarmed at the prospect of a no-deal departure from the EU.
“The resulting disruption to trade, access to labour and business stability would pose a fundamental threat to the viability of many of their businesses."
The union wanted the promised transition period to run for at least two years to ensure a smooth Brexit while also giving time for agreement to be reached on a future relationship between the EU and UK that recognised their mutual importance in terms of trade.
"With over 70% of our exports of food and non-alcoholic drinks being sent to EU markets, the NFU has been making the strongest case for a comprehensive free-trade agreement between the EU and UK," Soutar said.
"We were pleased to hear the prime minister say there is no intention to impose tariffs where none currently exist, which the NFU takes as a strong commitment to securing a free-trade deal with the EU.
"Any agreement should maintain, as far as practicable, the free flow of agri-food products between the EU and UK.
“Following the prime minister’s speech this remains a realistic prospect although much now depends on proper progress being made in the negotiations."
Sorting out future UK free-trade agreements with New Zealand and others seemed to be much further down the list of UK priorities, however, judging by their total exclusion from the PM's Florence performance.
