Home Secretary Priti Patel will push for the change in parliament next week.
British government is planning to label the whole Palestinian Hamas Movement as a terrorist organisation.
Home Secretary Priti Patel will push for the change in parliament next week, the Home Office said on Friday.
The al-Qassam Brigades military wing of the movement was banned in Britain since March 2001.
Patel argues she is pushing for the legislation as it is not possible to distinguish between Hamas' political and military wing
Patel, who is on a trip to Washington, said the move was "based upon a wide range of intelligence, information and also links to terrorism".
But Hamas spokesperson Hazem Qassem called the move "a crime against our Palestinian people and all their history of struggle, as well as a condemnation of the legitimate struggles of all free peoples against colonialism".
Qassem said the decision, if approved by parliament, would be "a great political, moral and legal sin committed by Britain" and only favoured Israel.
Israel's Prime Minister Naftali Bennett applauded the news.
"I welcome the UK's intention to declare Hamas a terrorist organisation in its entirety -- because that's exactly what it is," he wrote on Twitter.
Lapid said the move was a result of "joint efforts" between the British and Israeli governments.
Politically, it could force Britain's main opposition to take a position on Hamas, given strong pro-Palestinian support on the hard left of the Labour party.
Hamas is a Palestinian political resistance movement that presents itself as the defender of the people in Gaza Strip.
The group was elected by Palestinians in 2006, in the Legislative Authority elections defeating Fatah, and took control of Gaza in 2007.
Hamas, by many western countries, has been classified as a terrorist group over its failure to recognise Israel's right to exist and accept existing interim Israeli-Palestinian peace agreements.
According to other countries such as Turkey, Qatar, Russia and Pakistan, Hamas is a genuine resistance movement that challenges the Israeli aggression and keeps Palestine's legitimate demand for a separate statehood alive.