Royal Mail predicts that on what it calls Take-back Tuesday there will be a rise of more than 50% in returns against December's daily average.
Clothing and footwear are the most likely items to be returned.
People are also expected to flock to shops at lunchtime to give back gifts, but may face issues getting a refund.
Catherine Shuttleworth, from consumer analysts Savvy Marketing, told the BBC: "The problem for many people will be that without a gift receipt they will not be able to get a return at the retail price at which an item was originally purchased.
"Prices have been slashed in the Boxing Day and January sales, and there is also likely to be very mixed stock available if shoppers are wanting to return and replace an item, as it is unlikely a product will be available on the shelf."
It is not only shoppers who could have problems - there are also issues for the companies themselves.
"It poses challenges for retailers in terms of additional staffing for returns and ensuring that returns policies are adhered to," Ms Shuttleworth said.
"This year, returns are complicated by the high level of discounting before Christmas when many gifts were purchased - so retailers have the challenge of managing their [profit] margin on returns.
"You can also expect to see long queues in retailers at exchange points, which are never a desirable position for the retailer or shopper."
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Most online clothes shoppers send something back
Royal Mail's figures for the expected surge in returns is based on the number of parcels handled by its Tracked Returns service, which is used by more than 1,000 e-retailers.
A Royal Mail survey of 1,517 UK online shoppers, looking at the number of items sent back, discovered that 30% of them returned women's clothes, 17% men's clothes, 16% footwear and 7% children's clothes.
And in a separate survey of 1,505 online shoppers in the UK, 38% said that a free returns policy was likely to make them do more shopping in this way.
The highest volume of returns through Royal Mail in the last financial year took place in January 2016.
Post offices and shops are expected to be very busy on Tuesday, as people going back to work after the holidays try to return unwanted presents.