Rabbi Avraham Shmuel Goldberg was among the four people killed when two attackers stormed the synagogue, attacking worshippers with knives, axes and guns before they were shot dead by police, according to reports.
Mr Goldberg is a grandfather in his sixties who lived in Golders Green, north London, for many years before moving to Israel, according to Jewish News.
Israeli police confirmed a Briton died in the attack, while the three other victims were American. All four held dual citizenship after emigrating to Israel.
Foreign Secretary Philip Hammond joined US secretary of state John Kerry in condemning the attack, which occurred in Jerusalem’s Har Nof neighbourhood, an ultra-Orthodox area.
Speaking in London, Mr Kerry and Mr Hammond called on the Palestinian leadership “at every single level” to condemn the assault.
“To have this kind of act, which is a pure result of incitement, of calls for days of rage, of irresponsibility is unacceptable,” Mr Kerry told reporters.
Mr Hammond added: “Both sides in this conflict need to do everything possible to de-escalate the situation and reduce the tension we’ve seen in Jerusalem over the past few weeks, which is extremely dangerous for both Palestinian and Jewish communities in that area.”
The attack comes amid heightened tensions in the city, with a wave of attacks by Palestinians on Israelis in recent weeks, over .
Prime Minister Benjamin Netanyahu vowed that Israel will “respond harshly” to the attack, describing it as a “cruel murder of Jews who came to pray and were killed by despicable murderers”.
He blamed the attack on incitement by the Islamic militant group Hamas and Palestinian president Mahmoud Abbas.
However, Mr Abbas condemned the attack, the first time he has done so , but also called for an end to Israeli “provocations”.
His office said he “condemns the killing of the worshippers in a synagogue in west Jerusalem”. It called for an end to the “invasion” of the al-Aqsa mosque at the holy site and a halt to “incitement” by Israeli ministers.
The two Palestinian assailants were cousins from east Jerusalem. The Popular Front for the Liberation of Palestine said the cousins were its members. Hamas praised the attack and crowds celebrated in Gaza.