More than three in five people have been targeted by scammers posing as delivery companies in the past year, Which? has found.
The consumer rights group said fraudsters are exploiting the boom in online shopping caused by the pandemic by posing as couriers.
Nearly 80% of potential victims said they realised the text was a scam straight away, but 3% of those surveyed ended up losing money.
The most common scam involves a text claiming that a parcel couldn't be delivered and a small fee to pay for delivery.
This lures victims onto a fake website- seemingly indistinguishable from the courier's official site- where they are prompted to hand over sensitive information such as contact information or bank details.
Which? said that many victims then later received phone calls from scammers posing as someone from their bank and tried to trick them into sending large sums of money.
Our research shows how fraudsters have bombarded Britain with scam delivery texts on an industrial scale as they try to exploit the unprecedented conditions of the pandemic," said Which? consumer rights expert Adam French.
Couriers and the telecoms industry must take further steps to protect consumers by making it harder for fraudsters to exploit systemic weaknesses to reach potential victims and by making people more aware of how to spot such scams.
In the meantime, people can sign up to Which? 's scam alert service to keep themselves, their friends, and family informed about the latest tactics used by fraudsters.
To test the extent of the problem, Which? Researchers purchased four SIM cards from some of the UK's largest mobile suppliers.
Even though none of the mobile numbers had ever been shared or otherwise made public, two out of the four received nuisance messages within two weeks.
Before the pandemic, reports to Ofcom of problem text messaging had been in decline since 2015, as scammers moved with the times onto more popular messaging platforms such as the internet or data-led messaging services such as Whatsapp, reported Which?
However, the affordability and reliability of text messaging make it still a firm favourite with courier companies trying to communicate with customers about home deliveries, which have soared as the nation was forced to remain at home throughout successive lockdowns.
Spotting an opportunity, scammers have been quick to try and impersonate these companies.
Which? also warned of text messages containing malware known as 'FluBot', which is able to infect a device and harvest sensitive information when the message containing it is opened.
In December, Action Fraud reported that 166 victims has lost more than £139,000 since June due to scam courier texts.
Phishing messages are commonly used by criminals to gain access to our personal and financial details, leaving them free to commit fraud and take your money, said Head of Action Fraud, Pauline Smith.
Criminals are relying on the fact that we may need to reschedule a delivery to make their communication seem genuine.
If you think you've been a victim of fraud, you can report it at action fraud.police.UK or by calling 0300 123 2040.
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