Queen and Kate Middleton arrive for joint engagement in London

The Queen and the Duchess of Cambridge carried out their first joint engagement outside palace walls.

Kate, 37, and the Queen, 92, shared a blanket in the back of the car as they pulled up at King's College London, where they reopened Grade II-listed Bush House.

The Duchess was elegant in a grey Catherine Walker coat, believed to be a new bespoke addition to her wardrobe, which she teamed with her new favourite £510 Gianvito Rossi block heels and a black Mulberry clutch. 

In a rare move for such an outing, Kate, 37, completed her outfit with a hat, which is likely to be a sign of respect to the monarch. It is the same hat she wore when out with the Queen in Leicester in 2012.

Meanwhile the Queen, 92, plumped for a rose pink cashmere coat by Stewart Parvin and matching Rachel Trevor-Morgan hat with beautiful floral detailing at the brim.

Although they have carried out a handful of public visits with other members of the Royal Family, it was the first time that they have been on one together in public, outside of Buckingham Palace.  

In 2012 the pair visited Leicester as part of the Diamond Jubilee tour but were joined by the Duke of Edinburgh. However they did make individual stops on the schedule without him, including watching a student fashion show. 

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The Queen smiled warmly at the Duchess of Cambridge following a brief ceremony to officially open Bush House on Tuesday

The Queen smiled warmly at the Duchess of Cambridge following a brief ceremony to officially open Bush House on Tuesday

The Duchess of Cambridge carried a bouquet of pink, white and orange blooms as she left Bush House

Kate smiled warmly as she left the building this afternoon

The Duchess of Cambridge carried a bouquet of pink, white and orange blooms, left and right, as she left Bush House

The Queen and the Duchess of Cambridge shared a blanket as they arrived at King's College London in the back of a car

The Queen and the Duchess of Cambridge shared a blanket as they arrived at King's College London in the back of a car

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The Duchess of Cambridge threw her head back in laughter as they took in the views from the roof

The Queen smiled as she officially opened Bush House

Outside on the terrace which overlooked central London, left, Kate and the Queen both remarked on the 'impressive' view

The Queen unveiled a plaque marking the official opening of Bush House, King's College London, today

The Queen unveiled a plaque marking the official opening of Bush House, King's College London, today

The Duchess and the Queen both donned hats for the occasion

Kate had to readjust hers on the blustery roof

The Duchess and the Queen both donned hats for the occasion, left, although Kate had to readjust on the blustery roof, right

The Duchess of Cambridge remained by the Queen's side as she officially opened Bush House on Tuesday

The Duchess of Cambridge remained by the Queen's side as she officially opened Bush House on Tuesday 

The outing took place in March, shortly before William and Kate's first wedding anniversary. 

Later that year the Duchess of Cambridge joined the Queen at Fortnum & Mason for an event launching a military initiative, where they were joined by the Duchess of Cornwall. 

In 2014, Kate joined the Queen as she hosted a night in celebration of the UK's dramatic arts at Buckingham Palace. 

And in 2011, the Queen viewed Kate's wedding dress with her during a private tour of a new display at Buckingham Palace.

In June 2018, a few weeks after the royal wedding, the Queen carried out joint engagements with the Duchess of Sussex in Cheshire.

Today the Queen and the Duchess of Cambridge appeared in excellent spirits as they arrived at Bush House, which previously served as the headquarters for BBC World Service but is being leased by King's College London. 

It marks the newest building as part of the university's Strand Campus. 

Kate and the Queen could be seen sitting with a blue blanket over their laps as they arrived in the back of a car. 

The Queen and the Duchess of Cambridge have arrived at King's College London for a joint engagement

The Queen and the Duchess of Cambridge have arrived at King's College London for a joint engagement

The Duchess of Cambridge was handed a beautiful bouquet of flowers as she left Bush House following the appearance

Kate completed her outfit with a black hat, pictured, which she has previously worn on a number of occasions

The Duchess of Cambridge received a beautiful bouquet of flowers as she left King's College London following the outing

The Duchess of Cambridge waved as she followed the Queen out of Bush House, King's College London, today

The Duchess of Cambridge waved as she followed the Queen out of Bush House, King's College London, today

The Queen perfectly matched her outfit with her pink sapphire and diamond surround brooch, seen on her coat

The royal was also handed a bouquet of flowers as she left Bush House

The Queen perfectly matched her outfit with her pink sapphire and diamond surround brooch, as seen on her coat

The Queen and the Duchess of Cambridge spent roughly an hour at Bush House before leaving, pictured

The Queen and the Duchess of Cambridge spent roughly an hour at Bush House before leaving, pictured 

There was much fanfare, with well-wishers crowding outside the gates to the building and some even standing on bollards in the hope of getting a better glimpse of the royals. 

Following royal protocol, Kate waited for the Queen to leave the car before exiting the vehicle herself. She continued to walk behind the monarch as they made their way into the building. 

The royals were greeted by Lord Christopher Geidt, chairman of King's and former private secretary to the Queen, her most senior advisor.

He was ousted in a palace coup two years ago but remains close to the monarch. 

They were taken up to the eighth floor where they met donors, supporters and old alumni of the university who had contributed to transform the former BBC World Service at Bush House to a new faculty. 

The Duchess of Cambridge looked elegant in a Catherine Walker coat, black hat and black heels for the outing

The royal paired the piece with black tights and black block heels

The Duchess of Cambridge looked elegant in a Catherine Walker coat, black hat and black heels for the outing

Following protocol, the Duchess of Cambridge walked behind the Queen as they made their way into Bush House

Following protocol, the Duchess of Cambridge walked behind the Queen as they made their way into Bush House

The Queen and the Duchess of Cambridge appeared in excellent spirits and smiled as they arrived at Bush House

The Duchess of Cambridge cut an elegant figure in the grey tweed coat

The Queen and the Duchess of Cambridge appeared in excellent spirits and smiled as they arrived at Bush House

The Queen brought a splash of colour to proceedings in her pink coat and waved to royal well-wishers as she arrived

The Queen brought a splash of colour to proceedings in her pink coat and waved to royal well-wishers as she arrived

The Queen smiled as she stepped out of the car

She wore a coat by Stewart Parvin and matching Rachel Trevor-Morgan hat

The Queen smiled as she stepped out of the car, dressed in a coat by Stewart Parvin

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