Inflation, as measured by the Consumer Prices Index, rose by 0.3%. It was helped by smaller falls in food and fuel prices than a year ago.
Annual inflation has been below the Bank of England's 2% target for two years, and last year it was zero.
The BoE said earlier this month that it expected inflation to stay below 1% this year.
North Sea oil prices dropped to a 12 year low of $27.10 last month and have almost halved over the past 12 months.
But the Office for National Statistics measure of fuels and lubricants costs was only 7.3% lower than in January 2015, the smallest drop since November 2014.
Continuing low inflation makes the chance of an interest rate rise in the near future unlikely.
Few economists expect the BoE to raise rates before late this year at the earliest, and some analysts see a risk that the BoE could instead have cut to rates below the record low of 0.5% where they have been for almost seven years.
Financial markets do not currently expect interest rates to rise until the end of the decade due to concerns including a global economic slowdown and continuing low oil prices.
Food prices fell by 0.6% between December and January as opposed to a 1% fall a year earlier.
Supermarkets have been engaged in a long-running price war, and discounters such as Aldi and Lidl continue to take market share from the "big four" supermarkets - Tesco, Asda, Sainsbury's and Morrisions.
But the ONS said alcohol prices rose 5.2% between December and January, with spirits increasing by 7.5%, beer climbing by 3.6%, and wine up 4.8%.

The 26-year-old has been without a club since leaving Blackpool at the end of last season.
He started his career with Aston Villa before joining Scottish side Hibernian in August 2011.
Osbourne, who is new Iron manager Mark Robins's first signing for the club, could make his debut against Colchester on Saturday.

Wagner, 46, was appointed on a 12-month rolling contract in November 2015.
After a 19th-placed finish in the German's first season, the ex-Borussia Dortmund II coach led the Terriers to fifth last term before beating Reading in the Championship play-off final.
Wagner's assistant Christophe Buehler has also signed a new contract.
Huddersfield's first Premier League game is away to Crystal Palace on Saturday, 12 August.
The club have signed Belgian striker Laurent Depoitre and Australia midfielder Aaron Mooy, for a club-record fee, so far this summer.
Chairman Dean Hoyle told BBC Radio Leeds: "Without David being the coach of this football club last year, Huddersfield Town would not be in the Premier League. He defied all odds.
"The contract is a reward for the loyalty he has given the club."
UK inflation edged up to a 12 month high in January, as a fall in petrol prices eased.
[NEXT_CONCEPT]
Scunthorpe United have signed free-agent midfielder Isaiah Osbourne on a three-month deal.
[NEXT_CONCEPT]
Huddersfield head coach David Wagner has signed a new two-year deal after guiding the club to the Premier League for the first time.