Sales in December were up 1.5% compared with a year earlier, while like-for-like sales, which exclude new store openings, rose 0.3%.
Without a 17.8% jump in online non-food sales, total sales would have fallen.
“Since the beginning of 2011 we’re really not going anywhere,” said new BRC director general Helen Dickinson.
She added that there was little sign that things would improve in 2013.
The BRC bases its retail sales monitor on responses from its members.
“Many retailers have invested a lot in making their websites easier to use across devices and also increasing confidence in their online security… the surging popularity of tablets and smartphones giving even better access is a major factor,” Helen Dickinson said.
“For the more established retailers, it seems that much of the growth is now coming from online orders, while shop sales are stagnant at best.”
However, online retail was still only a small proportion of total sales, accounting for a little over 10%.
Aside from online, the one bright spot was department stores. On Tuesday, Debenhams reported record sales in December, while on Monday House of Fraser posted its “highest ever” festive sales. Last week, John Lewis also reported a sharp rise in Christmas sales.
“Department stores will always do well at Christmas, because they sell a lot of products under one roof,” Neil Saunders at retail analysts Conlumino told the BBC.
They have all also benefited from strong online offerings, particularly John Lewis with its click and collect service.
He also pointed to the fact that some established High Street names, such as Comet, are no longer trading, boosting sales at rival retailers. John Lewis, for example, “did extremely well in electricals”, he said.
“But this is not a sign that the market is growing, just a reallocation of sales.”
Mr Saunders also said upcoming trading statements from some big retailers would be less positive than those from the department stores.
“We have yet to have Marks and Spencer, which is not going to be great,” he said. He also highlighted supermarket chain Morrisons, which on Monday reported a fall in sales in December.
Official figures for retail sales in December will be released on 18 January.
The BRC also said the narrow gap between total sales and like-for-like sales was a sign of the small number of new store openings in 2012.
It said that the sales growth, which was flat after allowing for inflation, was making life difficult for retailers because rising costs meant they were “running fast to stand still”.
The flat reading on inflation-adjusted sales was the worst December performance since 2008.
It rounded off a tough year for UK retailers, when a number of big High Street names went into administration, including Peacocks, Game, Aquascutum, Clinton Cards and Comet.
Analysts said more were likely to follow.
“January will be a tough month for retailers as consumers face up to their credit card bills after Christmas, and it’s likely 2013 will bring more of the same challenges,” said David McCorquodale, head of retail at KPMG.
“There will be no boom and it is likely more than a few will go bust.”