Consumer price inflation (CPI) fell in January to an annual rate of 3%, down from 3.1% in December, official figures have shown.
The decline is less than expected - the consensus forecast was for an annual rate of 2.7%.
Prices continued to fall during the month as shops discounted heavily to try to entice consumers back into the shops.
The headline Retail Prices Index (RPI) fell to 0.1% from December's 0.9%.
The Bank of England has already cut interest rates to 1% in an attempt to stimulate the economy.
Another big factor in the fall in inflation was the cut in VAT from 17.5% to 15%, announced in the pre-Budget report in November.