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.”

It was billed as the great cheese-off: a helter-skelter, bone-jarring downhill race between the all-time champ and a young upstart.

After the hype and hyperbole, youth won out as the 24-year-old German YouTuber Tom Kopke beat the 38-year-old local hero Chris Anderson at the annual cheese-rolling event in the English West Country.

In his post-race interviews at the foot of Cooper’s Hill in Gloucestershire, Kopke said: “If that hill is hell, I’m the devil.” Anderson, tempted out of retirement by the challenge from Kopke, had taken the lead at first, but Kopke said: “I thought: ‘I’m going to get his ass.’”

He duly did, winning his third roll in three years, his prize the round of double gloucester that he and his fellow competitors had chased down the horribly steep hill. Asked to describe his method of preparation, he replied: “Shut off your brain and go for it.”

The pair embraced at the bottom. Anderson, who came second, admitted he had felt a little scared at the top and knew the game was up when he glimpsed Kopke haring past him.

The origins of the event are lost in the mists of time. Written records of it go back almost 200 years but Anderson, a ground worker who grew up in the village of Brockworth, home to the event, and has won 23 times, thinks it may have started 400 years before that. “Perhaps it was an old pagan ritual to bring good luck for the harvest,” he said.

Anderson’s tip for success is to refuse to sacrifice control for speed. “Obviously you need to be fast but overall it’s better to stay in control rather than going flat out.”

The event used to be a local affair but in recent years has morphed into something more global. Competitors travel from across the world and YouTubers and influencers attract millions of views by throwing themselves down the 1:2 gradient.

Kopke, who makes videos under the name Tooleko, has almost 500,000 subscribers and, as well as being a cheese-rolling veteran, has taken part in underground Thai fighting and reindeer racing.

Cheese-rolling has become so popular that the BBC broadcast this year’s event on iPlayer. The corporation had three reporters on the scene and two editing its live blog.

The race in which Kopke and Anderson took part was one of seven, staged over several hours. There were three men’s downhill races and one women’s. There were also less dangerous – but sweatier – children’s and mixed adults’ uphill races.

The second men’s downhill race was won by Niels Wennemars, 21, from the Netherlands, who was following in the family tradition of sporting excellence – as his father, Erben, and brother, Joep, are both world champion speed skaters.

“If you can stand and stay on your feet you will win,” he said. “If you live scared, you are going to die scared, and that is the worst way to live.”

The women’s downhill race was won by Alix Heugas, 27, from the Basque region of France. She said: “I had no technique, no training, just wing it. I’m going to eat the cheese with friends and family.”

The final race of the day was won by an American, 19-year-old Otto Linkogle, from Florida. “My heart was going and you just have to go,” he said. “I didn’t practise.”

The inherent risks of the event meant that the Tewkesbury borough safety advisory group officially declared it “unsafe”.

The council’s lead member for environmental services, Murray Stewart, said: “The cheese rolling is a unique tradition in our county and we have no desire to stop it.” But the safety group said a particular concern was how emergency services would be able to respond if there was a major incident with multiple casualties.

While the human participants often suffer bumps, bruises and worse, the cheeses generally fare well and are edible afterwards – even with this year’s very high temperatures. They are kept in a fridge until needed and carefully wrapped to make sure they remain intact.

Despite Anderson’s disappointment, his family still went home with a round of cheese after his son, William, won one of the children’s uphill races. The 11-year-old said he planned to keep the family tradition going by competing in the downhill when he was old enough.