Prince Harry in good spirits despite sleepless nights and missing his baby son

Proud father Harry was welcomed to the “sleep deprivation society that is parenting” by his brother the Duke of Cambridge after the birth.

But the prince was alert and in good spirits throughout his first day of royal events in the UK following the arrival of his son last Monday.

He took a tour of Oxford, starting with a visit to the city’s children’s hospital.

In a children’s cancer treatment ward, Christine George, 52, whose son James, 17, was having chemotherapy, said about Harry: “He said he had all this organised but had a sleepless night last night – not the ideal preparation for his first day at work.”

The duke also chatted to mother-of-two Amy Scullard, from Aylesbury, whose son Emmett, aged three, is in remission after being diagnosed with testicular cancer when he was two.

She was holding her 10-week-old daughter Ida and immediately struck up a conversation about Harry’s newborn son.

Ms Scullard said: “Harry asked me if she was over the stormy period as babies are supposed to be grumpy for the first 10 weeks – and she is.

“He said he’s getting used to the baby and how Archie has fitted into family life.

“He said he just feels part of the family and he can’t imagine life without his son.”

When the duke first arrived at the hospital, which is part of the John Radcliffe Hospital, he was presented with a tiny teddy bear for Archie.

Daisy Wingrove, 13, a former patient of the hospital, presented the gift to the duke just before he began his tour and Harry let out a big sigh and said “ahhh” as a nearby crowd of well-wishers made the same sound in sympathy.

During his visit, the duke had an emotional conversation with a mother, giving her a hug after he heard about her daughter’s cancer and posing for a photograph with her.

Sally Wade, 47, a nurse from Henley, Oxfordshire, said her daughter Georgia, five, was diagnosed with a kidney tumour seven weeks ago.

She said: “She has been having chemotherapy as an outpatient. She became unwell over the weekend so I brought her in.

“It turned out she needed a blood transfusion. Now she has got her energy back so hopefully we can go home today.”

Ms Wade also asked after Archie.

“I said: ‘What are you doing here when you should be at home?’

“He said, ‘It’s fine. He basically sleeps the whole time at the moment. He won’t know I’ve gone.’

“I said: ‘You must be totally in love with him?’ He said ‘yes I am’.”

Harry later visited the Oxsrad Disability Sports and Leisure Centre, opened by his mother Diana, Princess of Wales in 1989, where met people using the gym and undergoing physiotherapy programmes.

He ended his day in Oxford by touring the Barton Neighbourhood Centre, a hub for local residents which houses a doctor’s surgery, food bank, cafe and youth club, but went on a brief walkabout before going inside the building.

The prince spent around 20 minutes chatting to schoolchildren and residents including Fatma Sheikh, 43, from Oxford who could not resist asking the duke about his son.

She said: “Harry said Meghan and the baby are doing good and when I asked if he was sleeping a lot he said ‘yes’.”

Inside, Harry was told about the local food bank service and watched as staff filled bags with produce collected by the Oxford Food Bank, and chatted to diners at the centre’s cafe before unveiling a plaque and cutting cake to mark his visit.