The figure is above the three-month average of 1.9%, but below the 12-month average growth of 2.7%.
Retail sales in the UK increased by 1.8% on a like-for-like (LFL) basis during the month compared with the same period of last year.
For the three months to September, UK food sales grew by 4.6% and 4.2% on a total basis and LFL basis respectively.
Non-food retail sales for the three-month period declined by 0.4% on a total basis and 1.1% on an LFL basis.
In addition, in-store sales of non-food items increased by 2.2% on a total basis and 1.1% on an LFL basis.
During the month, online non-food sales dropped by 2.6% compared with a decline of 7.3% in September last year, while the non-food online penetration rate also declined to 38.4%.
BRC chief executive Helen Dickinson said: “While UK retail sales grew in September, this represented another month of falling sales volumes given high levels of inflation.
“A difficult winter looms for both retailers and consumers. Costs are increasing throughout retailers’ supply chain, the pound remains weak, interest rates are rising, and a tight labour market is pushing up the cost of hiring.
“All of this is making it harder for retailers to reduce prices and help struggling households.
“The industry urgently needs clarity from the government about business rates next year and is calling for a freeze in the multiplier.
“Without this, retailers will face an £800m hike in their bills, which will inevitably put additional pressure on prices for UK consumers.”
Last week, the BRC and Sensormatic IQ reported that total retail footfall in the UK declined by 9.8% last month against September 2019.