Parcel-delivery giant Evri has apologised after customers across the country were still not receiving packages on time or at all.
The firm said that staff shortages, Royal Mail strikes and bad weather had contributed to the problems and it was working to sort them out.
In December, Labour MP Carolyn Harris accused the courier of causing "misery" to people in the run-up to Christmas.
Evri, which used to be known as Hermes, said the backlogs should be cleared "over the next few days".
Customers across the country told the BBC they had not received parcels despite them being marked as delivered and others facing month-long delays.
More demand was placed on couriers when Royal Mail postal workers held strikes in the run-up to Christmas as part of a long-running row over pay and conditions.
Backlog
A spokesperson for Evri said the company continued to be affected by the backlog caused by the industrial action, as well as staff shortages and bad weather conditions.
However, it said it had managed to deliver more than "three million parcels each day over the Christmas period".
"Despite incredible efforts from all of our people, our service has not been as good as we would have liked, and we are committed to redoubling our efforts this year," a statement said.
Danni Hewson, an analyst at AJ Bell, told the BBC that Evri had been a "besieged" by the sheer volume of deliveries it had taken on.
She said Evri and other couriers faced a shortage of delivery drivers.
Ms Hewson added firms often employed temporary workers around Christmas when demand was at its peak, but said some of them might have opted to go for more secure and longer-term jobs, and were also more likely to take up seasonal work in supermarkets which offered higher pay and bonuses.
Criticism
As well as packages not arriving on time, customers have also criticised Evri's online help service and said getting hold of staff by phone or e-mail was extremely difficult.
Regulator Ofcom said the customer service some people experience when a delivery goes wrong "simply isn't good enough".
"Delivery companies will have to tighten up their complaints handling, and we're requiring better protections for disabled customers, who are almost 50% more likely to experience significant problems with parcel deliveries," the regulator said.
"If we don't see significant improvements in customer service, we'll consider enforcement action or tighten regulations further."