Reuters journalists on Thursday saw workers in the consulate remove a plaque reading "British Consulate General" and another sign for its consular section.
The British flag was still flying over the building, and there was no immediate comment from the consulate.
Israel in September ordered Britain to close the consulate within 30 days and remove its diplomats from the city after Britain announced sanctions targeting Israeli settlements in the occupied West Bank, including a trade ban on goods made there.
The United Nations and most countries consider the settlements to be illegal under international law. Israel disputes this.
Israel has been adamant the consulate will close even as Britain sought to keep it open, including sending the country's top national security adviser to Israel last week for talks.
Britain's presence in the city goes back almost 200 years, long before the State of Israel was established in 1948.
The closure order does not affect Britain's embassy in Tel Aviv, which handles diplomatic relations with Israel's government.
The consulate, in the Sheikh Jarrah neighbourhood of East Jerusalem, handles Britain's relations with Palestinians in Jerusalem, as well as in the West Bank and Gaza.
It also provides consular services to Palestinians.
Britain's Foreign Office on Wednesday declined to comment when asked whether the consulate was still operating or any British diplomats working there had returned to the UK.
Sources have said the order to close the consulate affects about 30 British diplomats along with their family members.
Britain is considering expelling Israeli diplomats from Israel's embassy in the United Kingdom in response to any closure of the consulate, Reuters reported on Tuesday, citing sources.
It would be a highly unusual step for the allies to expel each other's diplomats.
Despite the current strains, the UK and Israel are close economic, security and intelligence partners.
The British sanctions announcement, and Israel's order to close the consulate, mark a new low in a relationship that has deteriorated during the past three years.
Britain has repeatedly criticised Israel over its actions in the war in Gaza and over Israeli settler attacks on Palestinians in the West Bank.
Benjamin Netanyahu's government has accused Britain's governing Labour Party of being hostile towards Israel.
