The Duchess of Cambridge has carried out a rare joint engagement with the Prince of Wales and the Duchess of Cornwall.

The royal trio waved to members of the public together after visiting the Prince’s Foundation’s Trinity Buoy Wharf, a training site for arts and culture in east London’s Docklands.

Kate, wearing a grey Catherine Walker dress, joined Charles and Camilla as they met photography and animation students from The Prince’s Foundation School of Traditional Arts.

They posed for photographs against a backdrop of the River Thames and The 02 arena before the start of their tour.

They were shown the future textiles studio and pattern-cutting studio, which was once the old hemp store, where dock-workers made rope.

Graduates and entrepreneurs from the Modern Artisan project, a collaboration between the Prince’s Foundation and the YOOX Net-a-Porter Group, talked to Charles, Camilla and Kate about the techniques behind traditional kilt production and silk smocking.

Charles personally invited his daughter-in-law to join him and Camilla on the engagement because of her interest in and longstanding support for the arts and creative industries.

Kate’s patronages include the National Portrait Gallery, V&A and Royal Photographic Society.

The duchesses were given a cream sustainable silk pouch bag each and a pink scrunchie for Princess Charlotte made by Nicole Christie, a graduate of The Modern Artisan programme.

Miss Christie, 26, from East Kilbride, Scotland, has set up her own luxury womenswear line – Ellipsis.

She said: “I showed the duchesses my collection and I gave them one of my bags each that are due to launch in March.

“Everything is designed, patterned and handmade by myself. I don’t know what Ellipsis would have been if it hadn’t been for the prince.”

Miss Christie revealed that Kate, known for stepping out in glamorous evening gowns, particularly admired one of the full-length Ellipsis silk dresses on show.

The duchesses also spoke to two home-schooled sisters who joined a scheme with the Prince’s Foundation last year to learn fashion design.

Soukayna and Safiya Ouhammou from Woodford, London, showed them jumpers they are designing, inspired by photographs they took on their phones of lily flowers on the river behind the centre.

Kate said: “It’s fascinating to see how the whole process works, it’s a great idea.”

After being shown the sewing machines they use, Camilla said: “You’re obviously very good at this. I did it so long ago but I’m very bad at it now.”

The trio also joined a life-drawing class, although any potential blushes were spared as the model was fully clothed.

Camilla told 19-year-old Imogen Lewis from Suffolk: “It looks such fun. How long do you have to do it?”

Hildy Biernoff, 20, from London, said: “Kate told me she was amazed by all the different styles everyone has.

“She said when you step back and look at everyone’s drawings it shows a different aspect of their perception of what we are all seeing.”

Charles, a keen artist himself, stopped to speak to Hannah Ffytche, 19, from London, saying: “It must be very daunting when you have a blank page in front of you and a time limit. Where do you possibly start?”

Hannah said afterwards: “He was very interested in the life drawing and said he saw it as a connection to the natural world and everyday life, which is a good way of looking at it.”

The Prince’s Foundation runs courses at Trinity Buoy Wharf for all ages in traditional building skills such as thatching, blacksmithing and stonemasonry as well as associated skills such as geometry and sculpting.

The charity’s Future Textiles programme aims to bridge the gap created through the demise of sewing and textiles as part of the school curriculum.

Kate first carried out a joint visit with Charles and Camilla supporting the prince’s charities at the Dulwich Picture Gallery in 2012.