It added that a "new and improved" SFI, which will have a capped budget, will be set up but its details will not be announced until later in the year.
Daniel Zeichner, minister for food security and rural affairs, said: "This government is proud to have set the biggest budget for sustainable food produce in history.
"More farmers are now in schemes and more money is being spent through them than ever before. That is true today and will remain true tomorrow."
But Mr Bradshaw said the closure of the current SFI scheme had "slammed shut" the door for funding for thousands of farmers.
He said the closure was "delivered yet again with no warning, no understanding of the industry and a complete lack of compassion or care".
Victoria Vyvyan, the president of the Country Land and Business Association (CLA), which represents thousands of rural landowners, said that closing the scheme was the "most cruel" betrayal.
She added that the decision "actively harms nature. It actively harms the environment. And, with war once again raging in Europe, to actively harm our food production is reckless beyond belief".
Martin Lines, chief executive of the Nature Friendly Farming Network (NFFN), said the gap before a new SFI scheme is in place would leave some farmers "in a really difficult financial position".
"This has left many farmers feeling frustrated and let down, with no clear opportunity to be rewarded for delivering public goods in the near future," he said.