BBC Radio 4 Money Box reporter Dan Whitworth was phoned by a fraudster and managed to record the call.
The National Crime Agency says there's been "an explosion" in this type of impersonation fraud - when criminals spoof phone numbers to make it look like they're calling from genuine government departments or banks, for example.
Phone companies must do more to stop fraudsters who spoof phone numbers to trap victims, one of the UK's top law enforcement officers has said.
Graeme Biggar, director general of the National Crime Agency's National Economic Crime Centre, says the UK needs "a step change in our response" to fraud.
It costs the economy up to £190bn each year.
Phone companies say they are committed to taking action over nuisance calls.
Mr Biggar says there has been an "explosion" in the number of criminals spoofing phone numbers in the past 12 months.
"Phone companies have been used for fraud since they've been invented and it's a constant arms race to stop vulnerabilities and then stop them.
"With HMRC scams alone, more than 2,700 numbers have been taken out of circulation after they've been reported, but there is definitely a lot more that the phone companies need to do and can do."
His comments are backed up by a recent report from industry body UK Finance, which suggests the number of reported cases of impersonation fraud - including spoof calls - last year nearly doubled to 40,000.
However, the real figure is likely to be much higher, because many victims won't report fraud to their bank or building society, or even tell their family or friends, because of feelings of embarrassment or guilt.
Earlier this year, the level of fraud in the UK was labelled a "threat to national security".
What is number spoofing?
The communications watchdog, Ofcom, describes number spoofing as people who deliberately change the telephone number and the name that is relayed as the Caller ID information.
"They do this to either hide their identity or to try to mimic the number of a real company or person who has nothing to do with the real caller," explains Ofcom on its website.
"For example, identity thieves who want to steal sensitive information such as your bank account or login details, sometimes use spoofing to pretend they're calling from your bank or credit card company."
Ope Oladejo, a 21-year-old law student, had nearly £2,000 stolen from her last summer - money she'd been saving whilst working as a carer for help pay for a law course.
"The number spoofing was the most important part [of the deception]," she tells the BBC.
"At first I was a bit sceptical...but they said: 'Check the number [we're calling you on] on the back of your card'.
"I checked and it matched and that's when I let my guard down completely."
Because the criminals had convinced Ope she was speaking to her bank, they were able to get key details and information from her, which allowed them to steal the money.
Thankfully, the money was refunded by Ope's bank and she has been able to continue her studies, but she says the incident hit her hard.
"Emotionally it just made me really sad, I just cried a lot about it," she says.
"Financially I think it made me smarter... I basically ignore any phone calls I've not got saved as they might be a spoof."
The BBC approached Mobile UK, which represents the four big mobile phone companies, as well as BT, for comment.
The mobile operators and BT said they were committed to taking action against nuisance calls and to working with Ofcom and law enforcement bodies to reduce the threat.
They added that they take customers' security very seriously and advised people to hang up straight away if they are suspicious about any call.
Source: BBC News