Once a right of way has been established, the local authority and landowner are legally responsible for maintaining it.
Kate Ashbrook, general secretary of the Open Spaces Society, said if paths were not recorded developers might build on them or landowners might plant crops.
"We need to get those paths put on the map so we know where they are, so we can use and enjoy them," she said.
"The 2031 cut-off was designed to stop us from doing that and would have meant that all those public paths would have remained a secret, would have been lost."
The government is planning to repeal the cut-off date when parliamentary time allows.
However, NFU deputy president David Exwood said public access needed to be balanced with productive farming.
"This current plan simply perpetuates an outdated focus on routes that haven't been used for centuries," he said.
"Instead, the focus should be on a network fit for the future that encourages responsible use, respects working farmland, and promotes safety in accordance with the Countryside Code."
He added that the government's announcement did not provide a clear explanation of how the backlog of applications would be cleared, "continuing the strain on local authorities".
Ross Maloney, chief executive of the Ramblers charity, said the announcement ended "the threat to thousands of miles of historic rights of way in England".
"Not only are these paths an integral part of our shared heritage, but they will also have a critical role to play in the future by helping people live healthier, happier lives," he added.
Minister for Access Baroness Hayman said: "Our countryside and green spaces are a source of great national pride, but too many people across the country are left without access to the great outdoors.
"These well-trodden routes, many of which have been in place for hundreds of years, are a part of our shared heritage and it is critical that we bring forward these measures to protect their long-term future."
