This is a major step from Britain and a number of other countries against Israel, and one that puts them at odds with Washington.
It adds to the growing ostracisation of Israel over its war in Gaza and conduct in the occupied West Bank.
Read more: UK government sanctions Israeli ministers
Bezalel Smotrich is Israel’s far-right finance minister, a Jewish settler and someone who has denied the existence of Palestinians as a people.
He has most recently said “not a grain of wheat” should be allowed to enter Gaza, saying it will be “entirely destroyed” and its people should be encouraged to leave in great numbers to go to other countries.
Itamar Ben-Gvir, the country’s far-right national security minister, was once convicted of supporting a Jewish terrorist organisation and advocated the expulsion of Palestinians from their lands.
Their critics will say their sanctioning has been a long time coming, is largely symbolic, and will achieve little.
The British government singles out Israel’s conduct in the West Bank as grounds for its action against the two men.
Extremist Jewish settlers have run rampant across the occupied territories under Benjamin Netanyahu‘s government, with 1,900 recorded acts of violence against Palestinians since January last year.
The Netanyahu government has approved a record number of new Jewish settlements in the West Bank. Under international law, all settlements on occupied land are illegal.
Politics latest: Sanctions ‘a major step’
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Israel is increasingly isolated over its war in Gaza and actions on the West Bank.
The International Criminal Court has issued arrest warrants for Mr Netanyahu and other senior figures over alleged war crimes.
A number of countries and observers have deemed its conduct in Gaza as genocidal.
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Israel described the sanctions as unacceptable and outrageous.
However, critics will wonder why the Israeli prime minister is not sanctioned himself for keeping two such deeply controversial figures in his government.
There is, though, a good reason for keeping them.
Without them, his fragile coalition would almost certainly fall from power. The price for that though is only increasing.
