The Office for National Statistics (ONS) also said retail sales jumped by 1.3% between March and April beating analysts forecasts for a 0.5% rise.
Food sales during the late Easter holiday made a significant contribution to the overall figure, the ONS said.
They were 6.3% higher in April against a year earlier, and 3.6% up on March.
Non-food sales rose by 6.5% compared with a year earlier, but were down 0.4% on the month.
The annual rise in food sales was the biggest since January 2002, and were helped by a combination of better weather and sales promotions.
Increases in the price of food were limited to 0.9% in April, compared with 1.8% a month earlier.
Quarterly retail sales have now grown for 14 months in a row, the ONS added.
Howard Archer, chief UK and European economist at IHS Global Insight, described the latest set of figures as "mightily impressive", adding "this bodes very well for GDP growth in the second quarter".
He said: "The fundamentals for consumers are currently improving overall, and they should continue to do so over the coming months as employment rises further and earnings growth likely trends higher than inflation, thereby lifting purchasing power.
"The strong housing market is also supportive to retail sales."
And Ian Geddes, UK head of retail at Deloitte, said: "It is encouraging to finally see some strong figures in the food sector, as this remains a challenging market for the large grocers who are vigorously responding to consumers' changing retail habits and, are currently implementing significant structural reorganisation.
"This is clearly a long race and the large grocers are repositioning themselves to win over customers in the new, more complex era of multichannel retailing."
The retail figures come a day after official figures showed inflation increased to 1.8% in April, up from a four year low of 1.6% in March.
Meanwhile, the latest set of figures for average wage growth showed earnings grew by 1.7% in the year to March.
UK retail sales grew by 6.9% in April compared with the same month a year earlier, new figures show, making it the strongest annual rise in ten years.