How we met: Julia Peyton-Jones & Zaha Hadid

Zaha Hadid DBE, 62

Born in Baghdad, the Anglo-Iraqi Hadid (right in picture) is one of the world's most celebrated architects. London has been her base for the past 40 years, her most recent project being the Sackler Gallery, an undulating white canopy to the side of a Grade II-listed former gunpowder depot, as the latest extension to the Serpentine Gallery

Julia says we met in about 1994. I'm not very good with dates, but I do know that I became involved with the Serpentine in about 1995, 1996, when Lord Palumbo [former chairman of the Arts Council of Great Britain] invited me on to the Board of Trustees. I recall that I was asked to design a temporary space for a bookshop of theirs. It didn't happen, but then my role there was as an adviser. It was never part of my remit to design things for them.

But I have done just that now; in fact, three times over the years. The Serpentine is a very beautiful space for artists to exhibit their work. I think it's invaluable, actually.

In many ways, Julia and I are quite formal and professional with each other, but I do consider her my friend. We also have lots of friends in common, and we often all have dinner together. She's a tough lady, and very good at what she does. I'm sorry to say this, as I wouldn't want the Serpentine to lose her, but I do think she should be running a very major institution, whether in this country or abroad.

The work she does at the Serpentine is wonderful. I remember first being approached to design [what became the Sackler Gallery] many years ago by somebody else, but that never happened. So when the offer came again, I was very interested. It's quite a small space, and the scale is modest, but it is an important message, I think, to show that you can achieve beauty through modesty.

The whole design and build took about two years. It's always a tense time, full of budgetary concerns, time schedules, and so on. And we are both very opinionated people, but we do respect each other's opinion. There is no point having an adviser if you are not going to listen to them; they are the experts. If I go to a doctor, I'm confident he will give me the correct advice. Well, the same was true here.

As architects, we rarely go in with carte blanche, but we do have a lot of privileges. At the same time, however, you always have to address the client – in this case, Julia – and what is exciting about this profession is that, despite all the constraints, it's also a lot of fun.

It's always nice to complete a project. I tend to like to go somewhere hot and relax for a few months immediately afterwards. I haven't gone away yet, but then we haven't opened to the public yet, and that's why Julia and I haven't celebrated. The moment of reckoning comes when the public arrives.

Over the past 20 years, we have collaborated together three times. I expect and hope we will work together again.

Julia Peyton-Jones OBE, 60

Formerly a curator at the Hayward Gallery, Peyton-Jones has been a co-director of the Serpentine Gallery in London since 1991. She lives in London

Back when I first joined the Serpentine Gallery, the art world was a very different place. There simply wasn't the appetite for culture the way there is now, and certainly not for modern art. People would look at it and say that a child of three could do it; they don't say that now.

Redeveloping the Sackler Gallery here has been a twinkle in my eye for 15 years. I felt it was a once-in-a-lifetime opportunity to create not only a beautiful exhibition space thanks to Zaha, but also a restaurant that will surely come to be seen as one of London's best.

I must have first met Zaha in about 1995 or 1996. The Serpentine was closed for renovation, and so we moved to a temporary bookshop in Warren Street. It was tiny, really tiny, but we asked whether Zaha, who had recently become one of our trustees, would consider redesigning it. She already had a global reputation, but I felt sure she could do wonders with the space.

Anyway, for one reason or another, that didn't happen, but a few years later, in 2000, she redesigned our Pavilion. I was thrilled. I think what is so good about Zaha is that not only is she a great architect, but she is a great artist. All her work comes from extraordinary Constructivist drawing. Drawing is at the very heart of what she does.

She is a brilliant woman, and she is always very clear about what she wants. She is also incredibly supportive. I remember when my father died, she rang not only to express her sadness, but also to ask whether there was anything she could do. I thought that was enormously touching. Her loyalty is notable. You can go to any opening of hers around the world, and you are quite likely to find friends that she has had for years. She is good at keeping close connections with people.

Zaha has always been generous, and we are lucky at the Serpentine to be on the receiving end of that generosity. The architects and artists who work with us are paid only a stipend based on the visual-arts economy, not the architect's economy. In other words, she wasn't paid as much as she usually is.

But then [the Sackler] was an unparalleled opportunity to design a structure in one of the most beautiful parks in the world, right in the centre of London yet set among nature in historic Kensington Gardens. It has a profile that would be almost impossible to have in any other position. I think that what she has achieved here is truly beautiful. It has such a wonderful lightness of touch.

Each of the projects she has designed for us to date are like little jewels, tiny diamonds, each helping to make a great crown.

The Serpentine Sackler Gallery, designed by Pritzker Architecture Prize laureate Zaha Hadid, will open to the public on 28 September