Pete Comley, author of Inflation Matters, was interviewed on Share Radio on 17 February about why inflation is continuing to fall in the UK and the implications of that for consumers. You can hear the whole interview here (5 mins):
Pete states that inflation is so low primarily because of the decline in prices over the last year in motor fuels (-16.2%) and food prices (-2.8%).
But he notes that what drives the monthly change in the stats (i.e. CPI declining from 0.5% to 0.3%) also depends on what was happening to prices in the same period last year. If there was a big rise in an element a year ago, it would now fall out of the calculation. This can also make the rate appear to decline. For example, beer prices normally rise in January, but they fell this year. Similarly recreation and culture costs also normally decline in January but they did so much more this year (-0.9% in Jan 2015 vs -0.5% in Jan 2014). Both these helped drag down the annual inflation rate along with the prices of petrol and food.
More details on the numbers can be found in the full ONS report.