Parents were warned “swathes” of toys could be out of stock after the Black Friday spending spree.
Gary Grant, boss of toy chain The Entertainer, said shipments from China were taking around two weeks on average longer to arrive in the UK.
He said, while shops were well stocked at the moment, that could change after a flurry of buying for this month’s Black Friday discount event, which some retailers have already started.
“I don’t see shortages right now,” he told The Mirror. “But in the last two to four weeks (before Christmas) I think you will see swathes of things going out of stock.
“We are not saying panic but you will see more items out of stock before Christmas than you would normally.”
Mr Grant insisted that shortages were likely to result in smaller ranges of certain products. rather than empty shelves.
One item he said The Entertainer’s website was already sold out of was Moonshoes, after they proved a big hit.
There are growing signs that the widespread shortages that were feared have eased in recent weeks.
A number of retailers have recently reported that, while still a problem, congestion at ports had improved.
James Sawley, head of retail and leisure at HSBC UK, said his “gut feeling” was that retailers were on average getting around 90% of the stock they were expecting, up from about 60% in July.
He also predicted that with the easing of supply pressures and plenty of demand from shoppers, there could be fewer bargains over Black Friday and the run-up to Christmas.
“It will be a promotional event but the big discounts won’t be there,” he said.
Mr Grant also revealed his firm had bought in extra stock of big selling items in anticipation of price rises by manufacturers next year.