The newspaper said "Cobra," the government's emergency security committee, met several times as the MV Alaed approached British waters.
Cameron's advisers presented him with several options, including seizing and impounding the vessel, the newspaper reported.
Government officials instead gave orders ensuring the Alaed's insurance cover was withdrawn, avoiding a confrontation with Russia. The Daily Telegraph said the vessel changed course about 50 miles off the north coast of Scotland and was now showing its next port of call as Murmansk, the U.K. National Maritime Information Center said.
Western officials said the ship was carrying a military cargo including Hind-D Mi-25 helicopter gunships and anti-aircraft systems, but the ship's owners, the Russian operator Femco, denied it was ferrying arms to Syria.
"Reports about illegal actions of the Alaed's owner are inaccurate," Femco said in a statement. "The vessel is currently making a regular commercial voyage, in full accordance with international norms and rules."
Meanwhile, the Red Cross said it will try to evacuate hundreds of civilians trapped in and around the Syrian city of Homs, where activists said the situation was "desperate."
Violence in Syria Wednesday killed at least 60 people, more than a third of them government troops, the Syrian Observatory for Human Rights said.