Food prices were pushed higher by the rising cost of extra checks and requirements on EU imports, the LSE noted in the report.
On July 22, Ukraine and Russia signed a landmark deal with Turkey and the United Nations aimed at easing a global food crisis caused by blocked Black Sea grain deliveries.
Western countries have repeatedly pointed out that food is exempt from their sanctions on Russia and have blamed Moscow for the global crisis.
Lebanon is grappling with an unprecedented financial crisis, branded by the World Bank as one of the planet's worst since the 1850s.
Diplomats expect grain to start fully flowing for the first time since Russia's invasion of its Western-backed neighbour by the middle of August.
The Consumer Prices Index (CPI) jumped to 9.4 per cent last month from 9.1 per cent in May, the Office for National Statistics said in a statement.
Severe blow to food security efforts if Ukraine conflict does not give way to dialogue, diplomacy: India
World food prices are already climbing, and the war is making things worse, preventing some 20 million tonnes of Ukrainian grain from getting to the Middle East, North Africa and parts of Asia.
The continent relies on Russian natural gas, and higher energy prices are flowing through to factories, food costs and fuel tanks.
Experts have warned of a possible shortage of rice and other essential food items from September this year because of lower production.
Putin also said Western sanctions against Russia would only worsen world markets reducing the harvest and driving up prices.
President Vladimir Putin told Italian Prime Minister Mario Draghi that Moscow “is ready to make a significant contribution to overcoming the food crisis through the export of grain and fertilizer.
India certainly doesn’t own the copyright on export bans.
Russia and Ukraine produce a third of the world’s wheat supply, and the loss of commodities due to the war has resulted in soaring food prices and uncertainty about the future of food security.
German Foreign Minister Annalena Baerbock, who hosted a meeting of top G-7 diplomats, said the war had become a “global crisis.”
"Russia's war of aggression has generated one of the most severe food and energy crises in recent history which now threatens those most vulnerable across the globe," the group said.
Ukraine and Russia account for a third of global wheat and barley exports, leaving millions across North Africa, the Middle East and parts of Asia facing the potential loss of access to the supplies.
Ukraine and Russia account for a third of global wheat and barley exports, which countries in the Middle East rely on to feed millions of people who subsist on subsidized bread and bargain noodles.