The blasts, which caused damage but no casualties, were the latest signs of insecurity in Benghazi, the birthplace of the uprising that toppled Muammar Gaddafi in 2011.
The government has also struggled to keep order in the capital Tripoli, where the French embassy was bombed less than three weeks ago. Armed groups seized control of two government ministries a few days later to press demands on parliament and have refused to leave until the prime minister steps down.
"Given the security implications of the ongoing political uncertainty, the British Embassy is temporarily withdrawing a small number of staff," an embassy statement said, adding that the mission would continue to operate as usual.
A British embassy source said the decision was prompted by the ministry sieges, along with concerns that rival armed groups could clash at demonstrations organised in the capital.
Hundreds of government supporters marched on the Foreign Ministry in Tripoli on Friday chanting: "We will sacrifice our souls and blood for legitimacy."
A Reuters witness said that members of the armed group that has held the building under siege for almost two weeks scattered from its gates, while others retreated to the ministry grounds.
NO CONTROL?
On Thursday, the U.S. State Department issued a new travel warning for Libya and said it had ordered a number of U.S. government personnel to leave Tripoli for security reason.
The warning "strongly advises against all but essential travel to Tripoli and all travel to Benghazi, Bani Walid, and southern Libya, including border areas and the regions of Sabha and Kufra".
Benghazi has experienced a wave of violence against diplomats, military and police, including an attack in September that killed the U.S. ambassador and three other Americans.
The killings failed to inflict much political damage on the Obama administration but a congressional hearing this week provided an airing for opposition Republican accusations of negligence and a cover-up.
France, the United States and Britain, in an unusual joint statement on Wednesday, said Libyan institutions and elected representatives must be able to work free of armed intimidation.
"We call on all Libyans to refrain from armed protest and violence during this difficult time in the democratic transition," the three Western nations said.
The government turned to Europe's development bank on Friday for help in building institutions to fill the administrative vacuum left by more than four decades of Gaddafi's one-man rule.
For the time being, Libya is seeking only technical cooperation with the European Bank for Reconstruction and Development - a relatively low-level relationship with the bank.
Libya is not short of cash, but lacks the institutions and processes for spending the vast oil wealth it has accumulated.
More than two years after Gaddafi was slain, armed groups that helped topple him are still more powerful than the state in large swathes of the oil-producing North African desert country.
"The central bank governor said they have $130 billion in reserves but no state institutions," said a source close to Libya's discussions with the EBRD bank.
