The family of a 17-year-old who died while working as a Deliveroo rider - despite 18 being the minimum age - say the company is "unaccountable".
The Home Office is urging Deliveroo, Just Eat and Uber Eats to reform policies that let riders lend accounts to others, known as "substitution".
Deliveroo says it has a "zero tolerance approach" towards ineligible riders.
The BBC's investigation found substitution fuels an online trade in accounts, including potentially to children.
Riders who sign up to work for the big food delivery apps have to pass background checks. They must verify their age, that they have no convictions and that they are allowed to work in the UK.
But once verified, a rider is permitted to lend their account to another person to work instead of them.
It is the duty of the original account holder - not the app they work for - to check that their "substitute" meets the legal criteria to work.
The system appears open to abuse.
Leo was just 15 when he first rented his Deliveroo account from a man in the town where he lived.
Two years later Leo was killed on a borrowed motorbike - he was only 17 but still working for the app. The minimum age to work for the company is 18.
"Leo wanted to be a millionaire. Whatever it took, he just wanted to earn money and hustle," says Leo's stepfather Patrick.
His family have decided to speak out because they feel so strongly, but have asked to withhold their surname as they are worried about a backlash from riders in their local area who use illegal accounts.
Leo's mother Preta says on the surface the work was really appealing for a teenager. "They make a lot of money and they don't want to stop. Â£100 or Â£200 a day - it's a lot of money".
Patrick says: "No-one's accountable, they just take the money. It's not right."
Deliveroo has not contacted the family, he says.
"Well they wouldn't would they? They wouldn't even know he existed."
The company told us that if a rider was found to be ineligible to work for the app "we will stop working with them with immediate effect".
As part of our investigation, the BBC found social media account holders selling or renting accounts for the three main delivery apps.
We set up a fake social media profile, using an image of a 16-year-old boy generated by AI, and messaged the sellers.
When we told one seller offering Deliveroo accounts that he was speaking to a 16-year-old, he replied: "I want to help you, age does not matter."
Another said he would rent us his Uber Eats account for Â£70 per week, adding: "They don't check age, it's more like you are using my account."
Just Eat accounts were also available, this seller told us - "no one checks anything".
The company has the largest share of the UK market followed by Uber Eats and Deliveroo.
The government says it is unhappy with the situation and has called in the three big delivery apps for a round table meeting on Tuesday.
The Home Office also published an open letter to the companies calling for an end to "the use of unchecked substitution".
Home Office Minister Robert Jenrick told us: "This is not a victimless activity, we've seen a young person die when he was doing a job that he shouldn't have been doing."
Mr Jenrick said the policy of substitution was "perpetuating and enabling illegal working in our country".
And he called for it to be reformed so that any "substitute rider" would also be verified by the apps, not by the owner of the account.
The Home Office has been carrying out checks on riders and says, so far this year, 381 across the UK who do not have the right to work in the country have been arrested.
Deliveroo said: "We take our responsibilities extremely seriously and we continue to work in close collaboration with the relevant authorities to support their efforts in this area."
Just Eat released a statement saying: "We have high standards and a robust criteria in place for couriers.
"Self-employed independent couriers have the legal right to use a substitute.
"Legally the courier account-holder is responsible for ensuring their substitute meets the necessary standards to deliver on our network."
And Uber Eats said all couriers "must pass a criminal background check, be over the age of 18 and hold a valid right to work in the UK".
It added: "We understand that there are concerns around this issue, and we are working closely with the government and want to find a solution."
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A black-market trade in delivery app accounts allows underage teenagers to sign up as riders, the BBC has found.