Parents of nursery children in England are being charged extra fees to cover for government underfunding of free childcare hours, with some paying thousands of pounds a year for consumables such as food, wipes and nappies, campaigners have said.

The comments came as the education secretary, Bridget Phillipson, asked the competition watchdog to investigate hidden extra charges that parents have encountered when trying to access government-funded childcare.

Eligible working parents in England can get 30 hours a week of free childcare for children aged between nine months and four years old.

But the Department for Education (DfE) has said “too many” parents have reported being asked to pay more to secure a funded place, including on waiting-list deposits, compulsory add-ons and additional hours.

According to a survey conducted in May and June last year, nearly three-quarters of parents whose children were attending formal childcare reported having to pay for extras, including covering meals, drinks, snacks, nappies and sun cream, as well as one-off activities such as special outings.

“It’s a cross-subsidy,” Neil Leitch, the chief executive of the Early Years Alliance, an educational charity, told BBC Radio 4’s Today programme on Monday, as he sought to illustrate the scale of the problem for childcare providers – and the extent to which some were passing it on to parents.

According to one parent, Rick Kelsey, writing in the Times last year, as much as £16 a day – amounting to thousands of pounds a year for a child in nursery full-time – was being charged on top of the standard fees.

“I would love to see a toddler eat £16-worth of chicken nuggets and Babybel cheese before pickup,” Kelsey said. Referring to the article, Leitch acknowledged it was “not £16 per lunch. This is a cross-subsidy, basically.”

The results of the Ipsos poll last summer, which surveyed 2,000 parents of children up to four years old, suggested that more than a quarter found the cost of childcare was the “primary barrier” to accessing their preferred option.

Writing in the Guardian on Monday, Phillipson said “too many parents are still not feeling the full benefit” of the government-funded childcare hours.

“The vast majority of nurseries and childminders are doing a brilliant job – but we have to ask hard questions every time we hear stories of families hit with hidden charges, restricted hours or excessive deposits that bear no relation to what parents are actually paying. That is not what this investment was meant to deliver.”

In her letter to the regulator, Phillipson asked for details about the impact of extra charges on parents and providers.

In an effort to make accessing childcare simpler for families, the government has also recently launched a digital map of providers in Bristol, south Gloucestershire, Bath and north-east Somerset, which is due to be rolled out countrywide later in the year. The tool is available via the Best Start in Life website.

A Competition and Markets Authority spokesperson said: “We welcome the request from the education secretary to carry out a review into the early years childcare sector.

“The CMA has been monitoring developments and exploring the merits of work in this area. This is an important sector that needs to work well for families, and we will be developing a specific proposal to put to our board.”