The request for the evacuation came as the volunteers and their relatives were threatened by advancing forces of the Syrian government in the south of the country.
Foreign Secretary Jeremy Hunt said in a joint statement with the International Development Secretary that the "brave and selfless" volunteers required "immediate protection".
President Bashar al-Assad has called the White Helmets part of Al Qaeda in Syria. Israel agreed to evacuate the White Helmets "given the evident fact that Assad's rule is again taking hold in all of Syria", Israeli Regional Cooperation Minister Tzachi Hanegbi said in a radio interview.
"Words of condemnation are not enough to express the indignation that every Syrian feels towards these despicable conspiracies and the limitless aid from Western countries, Israel, and Jordan to the White Helmets", the source said.
The total number of people could be over 200, almost half of the Syrians evacuated into Jordan on Sunday. The US, while welcoming the evacuation of White Helmets in a statement penned by the State Department, didn't seem to be in a rush to welcome its members on its soil.
The White Helmets describe themselves as a volunteer workforce that acts to save people in Syria's war zones.
It added that the White Helmets supported "terrorists" and that the world had been warned of the group's "dangers", according to Syria's state news agency Sana.
Former UK ambassador to Uzbekistan-turned blogger Craig Murray has not been so glowing about the prospect of White Helmets members being granted resettlement in Britain.
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Air strikes by regime ally Russian Federation, meanwhile, on a southern jihadist holdout killed six civilians, the Britain-based Syrian Observatory for Human Rights (SOHR) said.
Some 98 White Helmets members were rescued by the Israel Defense Forces on Saturday night, as part of an evacuation mission that saw a total of 422 people collected from Syria and transferred across Northern Israel and into Jordan at three points, the Guardian reports.
The civil war in Syria has dragged on for more than seven years, resulting in hundreds of thousands of deaths and an unrelenting humanitarian crisis.
Huge plumes of smoke could be seen from the occupied Golan Heights just across the fence in Syrian territory as government and Russian forces launched air strikes and tanks shelled the area.
Piazza said Putin has made Syria the showpiece of its resurrection as a global superpower - and a player in the Middle East.
Evacuation plans were accelerated after last week's North Atlantic Treaty Organisation summit in Brussels. They were then escorted by Israeli and United Nations forces to a border crossing into Jordan.
The group are now in Jordan where they have been given temporary asylum.
More than 650,000 Syrian refugees are registered with the UN High Commissioner for Refugees (UNHCR) in Jordan but the kingdom says it hosts 1.3 million Syrian refugees.
Separately Sunday, al-Ikhbariya TV quoted a military official as saying that a military post in the town of Masyaf in Hama province was hit by an Israeli airstrike.