The measures impose strict financial and travel restrictions on the four individuals, who Britain said were involved in "egregious abuses of human rights".
"Extremist Israeli settlers are threatening Palestinians, often at gunpoint, and forcing them off land that is rightfully theirs," British Foreign Secretary David Cameron said.
"This behaviour is illegal and unacceptable. Israel must also take stronger action and put a stop to settler violence. Too often, we see commitments made and undertakings given, but not followed through."
Britain's Foreign Office said there had been unprecedented levels of violence by settlers in the West Bank over the past year.
The U.S. also imposed sanctions earlier this month on four Israeli men it accused of being involved in settler violence in the West Bank.
(Reporting by William James, Writing by Sachin Ravikumar)