Shadow defence secretary Clive Lewis demanded the tough response as the besieged city of Aleppo, where the convoy was heading, was targeted with fresh air strikes overnight.
Moscow and Syrian president Bashar Assad’s regime have denied their planes were involved in the air raid last week.
However, Mr Lewis told BBC radio’s The Westminster Hour: “If the Russians are found guilty of this they should have everything thrown at them, the full weight of international law.”
He added: “But at the same time we want to be seen with an even hand, then the British government, the Conservative government, should be playing the same way with Saudi Arabia.”
Dozens of air strikes hit Aleppo overnight, according to the Syrian Observatory for Human Rights.
“It’s the same situation. Especially at night, the bombardment intensifies, it becomes more violent, using all kinds of weapons, phosphorous and napalm and cluster bombs,” said Bebars Mishal, a civil defence worker in the rebel-held part of the northern city.
The Syrian army has launched a fresh offensive in the city which has become the main battle ground of the conflict.
The Observatory said it had documented the deaths of 237 people, including 38 children, from air strikes on Aleppo city and the surrounding countryside since last Monday when a week-long ceasefire ended. Of those documented deaths, 162 were in rebel-held east Aleppo city.