The businesswoman and mother-of-four said pocket money should be "earned, not expected," as new research found 85% of parents who hand out pocket money say their children don't always have to do anything in return for it, such as doing chores.
The survey, released by credit checking company Experian, also found parents rank celebrities above teachers as having a bigger influence on children's attitudes and behaviours when it comes to money.
While 68% of parents ranked themselves as having a big influence, 14% opted for celebrities, and just 10% opted for teachers.
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Willingham said money skills are essential for children, so when they eventually gain their first taste of independence and are offered credit, they can make good decisions.
She said: "What looks like free money, that's the problem. And with no plan of how you're going to pay it off.
"There's nothing wrong with credit when it's done properly. In the business world it's often essential. You've got to be able to deal with it and understand what it is that you're getting into.
"All we can ever do is give our children the tools to be able to make educated decisions. And what scares me is that we're not giving them the tools to make those educated decisions."
The survey found that 10 to 14-year-olds were the most likely to have to earn theirpocket money, although 81% of parents with children of this age said their children do not always have to earn their cash handouts.
Fifteen to 18-year-olds were the least likely to have to earn their pocket money, with 88% of parents of children in this age group saying they do not necessarily have to perform chores in return for cash.
Meanwhile, 86% of parents with children aged between five and nine who give pocketmoney said their children do not always earn the money.
More than half (59%) of parents who give their children pocket money do so every week, forking out £8.07 on average.
But one in 10 (10%) parents give out pocket money when their child asks for it - handing out £54.31 typically per time.
Willingham has worked with Experian to develop a free app called Jangle, which is aimed at children aged between seven and 11 years old and teaches them how to manage their money and save towards goals. The app has been quality marked by charity pfeg (Personal Finance Education Group).
The businesswoman said she would "never forget" the value of the money she earned from doing a paper delivery round as a youngster.
She said that the earlier parents start to introduce money skills to their children, the better, adding: "We (should) start to encourage good behaviour with money and teach children to have a very good and happy relationship with money very, very early on."
Willingham said that pocket money is a great way to start showing children how finances work.
She said: "By encouraging kids at a really young age to earn that money, not just handing it out, and to save for things is a great place to start, because often that conversation is child-led.
"I also think shopping is a brilliant (way of teaching children about money). I often say to my kids: 'Oh, can you go and get me some plain flour... bring me the cheapest,' or: 'Which of these tomatoes shall we get?'."
She added: "There are all sorts of ways kids can earn their pocket money, from washing the car to walking dogs - whatever works for you as a family. But the point is that pocketmoney should be earned not expected."
Willingham also said that financial know-how is vital for budding entrepreneurs.
She said: "I think it's cooler than ever to be an entrepreneur... we're seeing more and more mums get into it as well, which is fantastic.
"But again... it's just knowing where to go to get that help. It's knowing where to even start. It's there, it's just knowing which door to knock on."
More than 1,500 parents from across Britain with children aged from five to 18 years old took part in the research.