A fall in petrol prices contributed to the fall in inflation
Consumer Prices Index (CPI) inflation fell slightly in January to 3%, from 3.1% in December, figures have shown.
CPI inflation has now fallen for four months in a row from a high of 5.2% in September, driven down by falls in energy costs and fuel prices.
Retail Prices Index (RPI) inflation, which includes mortgage costs and is often used in pay negotiations, fell to 0.1% from December's 0.9%.
The drop in RPI may lead to pressure on employers to limit pay rises.
The headline RPI rate of 0.1% is the lowest rate it has been since 1960.
In addition to falling energy prices, the reduction in VAT from 17.5% to 15%, announced in the pre-Budget report in November, also had an effect.
The low level of RPI inflation could lead to some tricky wage negotiations.
"A zero or negative RPI could result in the extraordinary occurrence of average pay increases also falling towards zero," said John Philpott at the Chartered Institute of Personnel and Development.
In light of the current strain on government finances, Mr Philpott called for a freeze on public sector pay.
David Page, an economist at Investec, said wage growth would slow "quite markedly" this year.
However, he added: "It will be very hard for firms to push through wages growth at a lower level than 1% or 2%."
The modest decline in CPI was less than expected - the consensus forecast among analysts had been for an annual rate of 2.7%.
The falls in energy bills were slightly offset by rises in the price of household equipment, such as furniture, and alcohol, clothing and footwear.
The smaller-than-expected drop was also due in part to a reluctance by retailers to slash prices further after heavy discounting in December.
Jonathan Loynes at Capital Economics described the modest decline as a "temporary aberration reflecting the partial reversal of some very aggressive price discounting in December".
One of the reasons why the Bank of England delayed cutting interest rates last year was concern over inflationary pressures in the economy.
The bank has already cut interest rates to 1% in an attempt to stimulate the economy.
It believes that CPI inflation will drop to 0.5% this year and will remain below its 2% target for two years.
Others believe that core inflation could become negative this year, a situation known as deflation.
In the short term, this can provide a boost to the economy by increasing consumers' spending power, but in the longer term it can cause serious economic problems.
This is because consumers postpone spending as prices fall, which reduces companies' revenues.
If the economy does experience deflation, RPI, which stands at just 0.1%, is likely to become negative first.
"Next month, we'll see that measure move into deflation," said Ross Walker at RBS.
Many analysts expect the Bank of England to cut the Bank Rate by a further half percentage point in March to 0.5%.
However, with little scope for further rate cuts, the Bank is also expected to pursue a policy of quantitative easing, where it increases the supply of money into the economy.