The Duchess of Cambridge took a trip down memory lane when she spotted two faces she had not seen in almost 25 years during a whistle-stop tour of south Wales.

Kate was left surprised when she met her old prep school teachers during a visit to the Mumbles seafront in Swansea during a visit to learn about issues affecting the area and its people.

The chance meeting capped a day that saw the Cambridges celebrate local lifeboat crews, promote Kate’s early year survey, learn about Tata Steel at Port Talbot and spend time with children strengthening their mental health through boxing.

The duchess hugged Denise Evans-Allford and husband Kevin Allford who had travelled from their home in Carmarthen to meet Kate – the first time they have seen her in 24 years.

They both taught Kate, as well as siblings Pippa and James, at St Andrew’s prep school in Pangbourne, Berkshire. Mrs Evans-Allford taught PE at the school, while Mr Allford taught French and German to Kate.

Kate exclaimed “it’s such a small world” after seeing her old teachers following a visit to Joe’s ice cream parlour, run by the fifth generation of a family originally from Italy, where the duke and duchess were served sweet treats and met parents who had completed Kate’s early years survey.

“As they were coming to Wales today, we drove from Carmarthen to try to say hello to them,” Mr Allford said.

“One of the detectives took a note in to the ice cream parlour for us and she came out. It is wonderful she gave us so much time. We were talking about happy days that we had.”

William and Kate’s day in Wales began with hundreds of well-wishers greeting them when they arrived to tour one of the busiest lifeboat stations in Wales.

The Duke and Duchess of Cambridge visit south Wales
The Duchess of Cambridge speaks to members of the crowd as she leaves the RNLI Mumbles Lifeboat Station (Ben Birchall/PA)

The royal couple stopped to speak and shake hands with many of the members of the public who had come to catch a glimpse of the pair.

At the RNLI’s Mumbles lifeboat station, which overlooks Swansea Bay, the duke presented James Bolter with a medal to mark 20 years of service before watching the lifeboat launch as a part of training exercise.

The area’s biggest employer and one of the most important across Wales – Tata Steel – welcomed the Cambridges to its Port Talbot plant to learn about its role in UK manufacturing – from food cans to warships and cars.

The couple wore protective clothing including hard hats, goggles and a jacket for their guided tour of the plant’s Hot Strip Mill where some of its 4,000-strong workforce are employed.

The royals watched as ingots of steel were heated and passed through rollers which reduced their size in a process that produced a loud rumble and huge plumes of steam as the metal, glowing orange and radiating blistering heat, was coiled up.

The Duke and Duchess of Cambridge visit south Wales
The Duke and Duchess of Cambridge during a visit to the RNLI Mumbles Lifeboat Station (Ben Birchall/PA)

In the control room, known as the pulpit, the couple chatted to staff about the process and were told the steel they saw was being reduced to five millimetres in thickness would be used be used in car manufacturing.

Tata announced in November it would be cutting up to 1,000 UK jobs, part of a total reduction of up to 3,000 across Europe. The UK steel industry has battled against a glut of steel on the world market and other problems.

Before leaving, William chatted to Tata apprentices and told them: “Tata treat you well, that must settle some of your fears.”

The final stop for the duke and duchess was Port Talbot’s Bulldogs Boxing & Community Activities centre, where they spoke to children being helped through tough upbringings and mental health issues by boxing and fitness.

Kate took part in a teamwork exercise with some of the children, where the group stood in a line holding sections of a pipe and steered a small orange ball from one end to the other.

The Duke and Duchess of Cambridge visit south Wales
The Duke and Duchess of Cambridge look on at the mill during a visit to Tata Steel in Port Talbot (Toby Melville/PA)

The duchess was forced to poke the ball from her section into one held by a young girl next to her after getting into difficulty and joked: “Slight cheating.”

Club member Jasmine, nine, was approached by Kate after the exercise and spoke about using the centre.

Jasmine said afterwards: “She said it was nice coming to visit us. I told her, ‘You should never give up, you should persevere’, which is what they teach us here. You keep on trying and never give up.”

Samantha Fox, project co-ordinator at Bulldog Boxing, praised the royal couple for making the young members “feel really at ease” and said the gifts of boxing gloves and pads was “the most appropriate thing” to give them.

She said: “They were asking the young people about what they do here, asking what activities they take part in. They were really engaging, which is fantastic.”