The Consumer Prices Index (CPI) has dropped to an annual rate of 1.8% in June compared to 2.2% in May.
The Retail Prices Index (RPI) inflation measure, which includes mortgage interest payments and housing costs, fell to -1.6% from -1.1%.
The RPI is now at its lowest since the Office of National Statistic started records in 1948.
The Bank of England aims to keep inflation at 2% to maintain price stability and more broadly, economic stability.
Lower prices for meat, milk and fruit last month were the main reason for the fall in inflation.
The Office for National Statistics said: "A significant downward effect also came from furniture prices, which rose by less than last year.”
The CPI is far below what it was last September, when the rate hit 5.2% because of high oil and food prices.
The Bank of England is now predicting CPI will fall below 1% this year, as the downturn hits demand and sends prices lower.