Other issues revealed in the survey for Which? included parcels left in the rain and dishonest “attempted to deliver” notes left by drivers.
Delivery issues were reported by 54% of those questioned, while almost 17% said at least one of their deliveries failed to arrive on time.
It was more common for deliveries not to turn up at all, with 24% of online shoppers ordering an item that failed to arrive over the Christmas period.
The survey found that 24% of consumers had a courier who did not follow pre-arranged instructions – resulting in deliveries being handed to unauthorised neighbours or left in unexpected places.
And 9% said a delivery driver had left a note claiming the recipient was not at home when they were.
One person said they received a note claiming no one was at home after seeing the courier pass their home without attempting a delivery.
Which? consumer rights spokesman Adam French said: “Online shopping can take the hassle out of Christmas shopping but dealing with late, missing or damaged deliveries can be a nightmare for shoppers.
“Under the Consumer Rights Act, online retailers have a duty to ensure online orders are delivered within a reasonable time and in good condition, so if your delivery hasn’t gone to plan, don’t suffer in silence, and speak to your retailer to resolve the issue.
“But be aware if you give permission for your delivery to be left in a specified safe place, or received by a nominated neighbour, and something goes wrong, you will still be considered to have received the delivery.
“Think very carefully about those options when you’re making a purchase.”