The year-on-year sales growth, reported by the British Retail Consortium (BRC), is the fastest since last September.
Food sales were strong in January, according to the BRC, and technology items such as tablet computers and high-end smartphones were also in demand, as well as juicers.
The strong year-on-year growth in total retail sales value for January as a whole was achieved in spite of heavy snow in many parts of the UK during the month.
However, the BRC highlighted the part which discounting likely played in the strong January sales.
Edinburgh-based David McCorquodale, head of the UK retail practice of accountancy firm and BRC survey sponsor KPMG, said: "It's a strong start to what is anticipated to be a tough year for the sector.
"Many retailers will be pleased with their sales campaigns as 2013 roared into life, producing double-digit (percentage) sales increases in several categories in the first week."
However, he added: "Sadly, a blanket of snow mid-month slowed the charge as payday approached."
News of the better January sales follows disappointing figures recorded by the BRC for the key trading month of December.
The BRC had noted a month ago that retail sales volumes in December were flat year-on-year, taking into account annual shop-price inflation which the industry body calculated at around 1.5%.
In December, the value of sales north of the Border was also up just 1.5% on the same month of 2011 – according to figures published by the Scottish Retail Consortium (SRC).
This indicated retail sales volumes were flat year-on-year in Scotland, as well as in the UK as a whole, in December. The SRC will publish Scottish retail sales figures for January next week.
Mr McCorquodale, highlighting the part which promotional activity had played in driving sales in the food sector last month, said: "Targeted promotional campaigns from the grocers fighting for market share helped drive strong January food sales."
Commenting on the general picture, he added: "Many retailers will look back at the last two months with pride, after implementing successful seasonal campaigns where they have served the customer well."
However, he cautioned: "Sales are only one side of the equation, and time will soon reveal the true cost of the promotions and (profit) margin squeezes used to drive these sales."
Although he cited this pressure on margins, he said of the January retail sales figures: "It is encouraging to see such positive results in what is traditionally a challenging month."