The BRC data, which covers the four weeks from 4 April to 1 May, shows a 28.7% improvement from the previous month.
It is also above the three-month average decline of 59.2%.
The increase in footfall follows the easing of lockdown restrictions in the country and the reopening of retail and some hospitality on 12 April.
BRC chief executive Helen Dickinson said: “[The return of customers to shops] is reflected in the improving levels of footfall seen across the country, as consumers visit their favourite stores post-lockdown.
“Retail parks continued to fare better than shopping centres and high streets, as they benefit from the presence of large stores, more space and on-site parking. But it was encouraging to see footfall improve across all retail sites compared to the lockdown months.
“Growing consumer demand and footfall in the months ahead will be vital for the survival of many retailers, as they start to see costs increasing as stores reopen and colleagues return from furlough.
“With full business rates relief ending in England in June, the ongoing rates review needs to deliver on its objectives to reform the broken rates system and reduce the financial pressures on retailers, otherwise many stores and viable jobs will be under threat.”
Despite this increase in footfall, the figure is still 40% below pre-pandemic levels in 2019, according to Sensormatic Solutions Europe, Middle East and Asia (EMEA) retail consultant Andy Sumpter.
Mr Sumpter said: “Retailers will be hoping that the lift in shopper traffic seen during the first few weeks [after 12 April] can be sustained past pent-up demand in order to fuel long-term recovery.
“Our research shows an overwhelming amount of consumer support for bricks-and-mortar retail, with 71% of shoppers vowing to make a conscious effort to shop in-store now retail has reopened.
“Many shoppers missed the experience of in-store shopping after lockdown shuttered shops and other saying ‘screen fatigue’ had set in.
“Retailers will be counting on shoppers acting on that sentiment and voting with their feet to support the shops that serve their communities.”
In March, the BRC urged the UK Government to preserve retail jobs amid reports of heavy losses.
According to data from the Office for National Statistics (ONS), retail jobs in the UK had fallen by 67,000 year-on-year to 3.1 million.