Britain's Foreign Office said the footage was discovered on a mobile phone found in the wreckage of a crashed government forces helicopter and handed to broadcaster Al Jazeera.
"This video footage exposes Assad's lies on barrel bombs. It shows the casual and indiscriminate way in which Syrian regime forces are dropping these horrific weapons out of helicopters onto civilians below," Hammond said in a statement.
"We will bring those involved in these criminal acts to justice and will continue to help those caught in attacks by continuing our support of rescue teams working on the ground."
According to Amnesty International, barrel bombs -- containers packed with explosives and projectiles that are dropped from helicopters -- killed some 3,000 civilians in the northern Aleppo governorate last year.
Assad said in February that the Syrian air force did not use barrel bombs. U.S. and European officials have said his denial is not credible, and Hammond's intervention reflects growing Western anxiety about the issue. (Reporting by Kylie MacLellan; Editing by Andrew Osborn)