TV ads for payday loan companies could be banned before 9pm under a bill tabled by the Bishop of Truro.

The Rt Rev Tim Thornton has proposed a law that would see adverts for companies like Wonga forced to air after the watershed. It is hoped that this will reduce the risk of children being exposed to dangerous messages about money.

"While many parents are struggling to pay the bills, payday loan adverts are making borrowing money seem easy and fun to their children. This is creating 'pester' pressure on parents to take out high-interest loans," the Consumer Rights Bill – issued jointly with Lord Alton and Lord Mitchell – reads.

"As credit repayments take up a larger proportion of income, families can be pushed into problem debt and find themselves cutting back on essentials. We know that children living in families trapped by debt can suffer worry, anxiety and even bullying as a result of their family's financial problems."

Currently before the House of Lords, the bill will be voted on this Wednesday.

Bishop Tim serves as chair of the trustees of The Children's Society, a charity that earlier this year called for Ofcom to ban payday lenders from advertising during television programmes aimed at children.

An online petition accused lax advertising rules of "increasing the pressure on families...struggling with unmanageable debt."

Branding such advertising as "unethical", the charity said the practice "must be stopped" – a challenge that was backed by Citizens Advice and Labour leader Ed Miliband. However, the government ruled out a complete ban in March.

The Children's Society at the time said it was "disappointed" with the response.

The latest challenge to payday loan companies follows the launch of the Archbishop of Canterbury Justin Welby's credit union scheme to take on and outdo unscrupulous firms.

The To Your Credit initiative will, Welby said, help people to deal with their finances "as a servant, not as a really cruel master".

"All of us from time to time need access to some financial flexibility. But in recent years, it's been quite hard to get that at reasonable cost. The To Your Credit initiative is seeking over time to make good finance, both to save and on occasion to borrow, available to everyone at a reasonable cost. It's to get away from people who seek to take advantage of other people's needs," he added.

The Church of England announced in July that it had cut all its ties with Wonga after facing criticism for its investment in the payday lender's portfolio.