Jeremy Hunt, the health secretary, has told the private memorial service for a one-year-old boy who died from blood poisoning that the child was let down by the NHS and the government.

Speaking at the service in Cornwall, Hunt said he had “come here to say sorry” to the family of William Mead, who died after the emergency services failed to diagnose a fatal case of septicaemia.

Hunt told those gathered at Truro Cathedral in Cornwall: “I as health secretary, the government, and the NHS, let down William.

“I’ve come here to say sorry. This weekend William should have been enjoying beautiful Cornish sunshine with his parents.

“We didn’t spot his sepsis before it was too late.”

William’s mother, Melissa Mead, has become a prominent campaigner for better diagnostics of sepsis, saying last year that the NHS system was “broken”.

She has also described her son’s final hours, his symptoms and her repeated pleas to health services in painstaking detail on her blog site.

An NHS England report revealed there were 16 mistakes associated with William Mead’s death. Photograph: PA

The health secretary became aware of the case last year and has taken a personal interest in Mead’s campaign, a Department of Health spokesman said.

The spokesman added: “He went down at the request of the family and was also down there to visit a hospital. He had obviously become quite close to Melissa and they have worked quite a lot on the campaign on sepsis.”

An NHS England report last year found there were four missed opportunities to save William’s life in December 2014. Doctors and the 111 non-emergency helpline failed to diagnose pneumonia and the common but lethal infection of sepsis, and he died within 12 hours of Melissa Mead’s last call.

The report found there were 16 mistakes contributing to his death, which included that the “tickbox” system used by call handlers failed to include “sepsis red flags”.

It added that doctors were under constant pressure not to prescribe antibiotics and that doctors working out of hours were unable to access patients’ medical records.

RT: Official Sepsis Public Awareness Campaign Video. Do you know the #SymptomsOfSepsis Please watch & RT to help us save thousands of lives. pic.twitter.com/5jV6ePxBaO — Melissa Mead (@amotherwithout) December 14, 2016

Sepsis – which includes common symptoms of fever, increased heart rate and confusion – kills approximately 37,000 people each year in England.

Melissa Mead said on Sunday: “We invited Jeremy to William’s memorial as he’s played a pivotal part in the sepsis campaign and we couldn’t have got it off the ground without his government support.

“Jeremy agreed to come in a personal capacity and it was a very intimate event for friends and family. The relationship that we have shows how productive a constructive approach can have.

“We know William was let down, but William didn’t know blame or regret, only love, and it is with this love that we keep putting one foot in front of the other.”

Hunt has admitted letting the family down and in January 2016 Mead welcomed his apology then.

She said: “We are quite overwhelmed, to be honest. We are just a little family from Cornwall but William is going to make an impact on the world and we are very thankful for that.”

The Department of Health spokesman added that Hunt was working with Mead’s awareness campaign in conjunction with Public Health England and the UK Sepsis Trust.