The BRC also warned that the changes could cost retailers up to £14bn over the next four years.
The report said: "However, the effects will be uneven across the country and in how they impact on different sizes of business and groups of people within the industry.
"Areas that are already economically fragile are likely to see the greatest impact of store closures and some of the people affected by changing roles will be those who may find it hardest to transition into new jobs that are created."
The study said smaller retailers "generally have fewer ways in which to respond and are therefore likely to be more affected than larger retailers".
The BRC estimates a cost to the industry of up to £3bn per annum.
"With the introduction of the National Living Wage, labour costs are now set to rise," the BRC report says.
Garden Centre Association chief executive Iain Wylie said online shopping was another issue that would mean lost retail jobs. He said NLW would mean pay differentials could narrow between trained and untrained staff and that businesses would need to find cash quickly to pay for the hike, which comes in on 1 April.
BRC wants: Rebalance the burden of taxation, by fundamentally reforming the business rates system.
#Ensure the remit of the Low Pay Commission is strengthened and clarified with regard to the National Living Wage.
#Greater employer leadership of the apprenticeship levy including more discretion for employers over how and where it is spent.
Meanwhile, the Federation of Small Businesses has called for the Chancellor's Spring Budget to back enterprise, reform business rates and simplify taxes.
In its submission to the Chancellor of the Exchequer in advance of the 2016 Spring Budget Statement, the Federation of Small Businesses said its recent quarterly survey shows small business confidence is cooling "in the face of deteriorating global economic headwinds and domestic policy decisions which are coming into force".
FSB said: "Our members are being tested by a series of significant challenges which will drive up costs and increase burdens over the coming months. These include the introduction of the National Living Wage in April, pension auto-enrolment and changes to the tax treatment of dividends. On top of these, small firms still face an unreformed business rates system and the prospect of compulsory quarterly digital tax reporting.
"Three weeks ago, the Chancellor spoke to FSB members at our Policy Conference stating he would back small business. FSB calls on the Chancellor to use his Budget to do just that – to boost business confidence, to deliver fundamental reform of business rates and to simplify the tax system."
Business rate reform of the non domestic rates (NDR) system is top of the agenda.
FSB has put forward a recommendation which would see businesses occupying low value hereditaments with an assessed value of less than £12,000 being removed from the rating system entirely. This would free up the appeals system from high numbers of low value claims, helping to support cash-strapped local authorities.
In addition FSB have suggested the following measures:
• For those business premises which remain in the NDR system, we recommend more frequent valuations and a fixed national multiplier . This should allow for a more rapid response to changes in economic conditions.
• The current proposals for reform of business rates appeals will increase the burden on small firms. Fundamentally, ratepayers should know how their rateable value is calculated before lodging an appeal.
• Removing the disincentive to invest in new or improved business premises.