Jeremy Browne said the incidents were “appalling” and people would be “shocked” by the footage of the February 24 and 26 attacks.
“The Libyan authorities themselves are shocked too,” he told Sky News television.
“We have had direct dealings with them. They have been extremely apologetic and made a very strong commitment they will get to the bottom of this happening. They will try and do everything they can to resolve it.
Video footage shows a mob smashing up headstones and a cross of sacrifice, saying “they are dogs”.
Local reports said the group comprised Salafists angered by the burning of the Koran at a NATO military base in Afghanistan last month.
The Libyan transitional government on Tuesday condemned the attacks and vowed to find the perpetrators.
Some 1,214 Commonwealth troops who died in the north African desert battles of World War II are buried at the Benghazi War Cemetery, where around 200 headstones were damaged.
Of the 1,051 identified graves, 851 are those of British troops, with others belonging to Australian, Canadian, New Zealand, South African and Indian servicemen.
Around a quarter of the headstones in the nearby Benghazi British Military Cemetery, which does not contain World War graves, were also damaged.
“My understanding it is not just British graves or just Christian graves that have been desecrated, there is wider desecration taking place. The Libyan authorities are keen to work with us on this,” the minister said.
The British and French air forces last year aided Benghazi-based rebels to oust dictator Moamer Kadhafi from power after his tanks encircled the city.
A Foreign Office spokesman told AFP that Britain’s ambassador in Tripoli has spoken to Transitional Council chief Mustafa Abdel Jalil and Libyan Prime Minister Abdel Rahim al-Kib about the attacks.
The Commonwealth War Graves Commission, which maintains the cemeteries, said it would restore them.
“We are awaiting a detailed report but in both cemeteries, headstones were broken and disfigured,” the intergovernmental body said.
“Both cemeteries will be restored to a standard befitting the sacrifice of those commemorated at Benghazi, but this could take some time because we will need to source replacement stones.”
The commission said temporary markers would be erected over the graves and no detailed work would take place before they were sure it was safe.