Prior to the unveiling of their art world coup – the only UK venue to host an exhibition of paintings by both Frida Kahlo and Diego Rivera side-by-side – Pallant House Gallery found itself in the middle of a stormy argument.

A piece in The Guardian’s G2 supplement on Wednesday, June 29, reported the outrage felt by American artist Judy Chicago, who said: “By looking at her [Kahlo’s] art in relation to Rivera, rather than for itself, she is kept in a place where she is a lot less challenging than she might be.”

It’s an argument that Pallant House Gallery director Stefan van Raay feels mystified by.

“I don’t see that argument at all,” he says on the day before the exhibition opened.

“Rivera was the person who really stimulated her to paint, and to go on painting after her first miscarriage.

“Mexico didn’t recognise her work, but he was convinced she was a great artist.

“There is painting after painting which is iconic and depicts the two of them together, in an embrace. We can’t detach ourselves from their story.”

When Rivera and Kahlo were married in 1929, it was the 42-year-old Rivera who was the household name in Mexico, largely because of his large-scale murals painted in Mexico City.

The pair met when Kahlo showed him some of her work, having begun painting after an horrific trolley bus accident on the way home from school in 1925 left her bed-ridden for months at a time.

While Rivera’s paintings were frequently on a grand scale, hers were often limited to the size of canvas she could prop up in bed, using a special easel her mother made for her.

Size isn’t the only contrast between their painting style. Rivera’s early paintings, until 1917, were in the Cubist form, painted while he was in Europe. He gave the form up altogether, returning to figurative painting, after meeting the fellow mural painter David Alfaro Siqueiros in Paris, full of stories from his time on the Mexican battlefields. The pair travelled to Italy before returning home to Mexico in 1921.

“Rivera was incredibly interested in what was going on in his homeland,” says van Raay.

“His travels in Europe meant he had seen the Renaissance murals of Italy. He also knew Mayan art, and from those two elements he was able to create his personal muralist style.”

Kahlo’s pictures are much more personal, with more than a third of her 143 paintings being self-portraits, full of surreal touches and Mexican cultural references which make them look and feel exotic and ahead of their time, especially to Western eyes.

“She paints her own reality,” says van Raay.

“Her radius was smaller compared with Rivera, she was very restricted with what she could do.”

Kahlo herself said, “I paint self-portraits because I am so often alone, because I am the person I know best.”

Both painters have a striking use of colour and incorporate the imagery of Mexico. But their differences can be seen in the one pair of paintings which are subtly matched in the exhibition – portraits of art patron Natasha Gelman, commissioned by her husband Jacques in 1943.

Rivera’s almost life-size portrait presents her as a Hollywood starlet, stretched across a chaise longue, in a glamorous white dress, dripping with jewelley and framed by his favourite flowers, calla lilies.

Through a doorway, Kahlo’s portrait of the same lady can be seen – a small oil painting focusing solely on Gelman’s face and head, making her look pretty but real, without the soft focus glamour of Rivera’s portrait.

The decision to separate the pair’s work was deliberate. Each has their own separate space, while the final room of the exhibition focuses on works by Kahlo that examine her relationship with Rivera, ranging from larger works depicting both artists together, to paintings on pages ripped out from Kahlo’s diaries.

“I didn’t want to mix the two as there is such a difference between them,” says van Raay.

“What really binds them is their convictions and their admiration of each other.

“Each had an incredible love for Mexican history and their Communist comrades, but the way they expressed it in their art couldn’t be further away from each other. It just wouldn’t work to combine them.”

Many of the resonances in Kahlo’s work come from her deeply personal subject matter.

The exhibition features pieces she painted while in emotional agony after her first miscarriage in 1925, including her Self Portrait With Necklace and Self Portrait On Bed featuring Kahlo lost on an iron bed alongside a doll – perhaps substituting the baby she never had.

Many of the paintings follow the Mexican tradition of ex-voto paintings – scenes of illness, accident or disaster where the subject is rescued by divine or saintly intervention, usually painted on metal.

These paintings have an extra resonance to anyone with a knowledge of Mexican culture. Kahlo wasn’t unknown as an artist while she was alive – her work was shown in public in Paris, New York, Boston and Mexico City during her lifetime – but it was often down-played.

For example, there was a contemporary Detroit News article which interviewed her entitled “Wife Of The Master Mural Painter Gleefully Dabbles In Works Of Art”.

When someone bought one of her paintings Kahlo is reported to have said: “For that price they could buy something better”.

Why Kahlo is now much more famous than her husband van Raay puts down to two factors: feminism and multi-culturalism.

“She has been championed first by schools of feminism focusing more on women in art,” he says.

“And she has been very attractive to multi- culturalism, as she is German, Spanish and Mexican.

“In the 1930s in Europe there was a move towards a kind of surrealism, and she fitted into that well, but she reinvented European painting.

“Kahlo refused the label of surrealism. Andre Breton wanted her to become a member of the Surrealist movement, but she said she would ‘rather sit on the floor in the market of Toluca and sell tortillas than have anything to do with those ‘artistic’ Parisien b******’. She painted her reality, but Mexico is a fairly surreal place. I call her work magic reality.”

Further insights into theworld of Kahlo and Rivera are present elsewhere in the gallery.

The first-floor landing features two walls of black and white photographs by Kahlo’s father Guillermo, depicting churches and cloisters around Mexico City and Tepoztlan.

“There was a strong link between daughter and father,” says van Raay.

“Kahlo was able to work in her father’s studio and look at portraiture, photography and things like that.

“The famous Blue House, where Kahlo and Rivera lived, was Guillermo’s originally. They took it over when he died.”

The main exhibition also gives other views of Kahlo and Rivera through contemporary photographs. There is an image by Silberstein Bernard of Kahlo painting her self-portrait Diego In My Thoughts, which itself features as part of the exhibition. Other beautiful colour photographs come courtesy of Kahlo’s lover of ten years, Nickolas Muray.

Kahlo’s face in her self-portraits is unforgettable – it seems to stare out of paintings with a burning intensity. The photographs give different viewpoints of the painter, while at the same time underlining her iconic look, complete with unibrow and love of Mexicanidad – traditional Mexican clothing.

In the flesh we see her distracted with cigarette in hand on a New York roof, or with a smile flickering on the edges of her mouth in Frida On White Bench.

Across from the exhibition is a selection of images by another Mexican husband and wife team, Manuel and Lola Alvarez Bravo, who give other views of Mexico through their black and white shots.

There are strong links between the couples: Lola hosted Kahlo’s first solo show in Mexico City in 1953.

And like Rivera, Manuel was honoured in his lifetime in his home country as the “poet of the lens” for work which mixed the surreal with iconic images of Mexico.

But that this exhibition of Kahlo and Rivera exists at all is down to two people – Jacques and Natasha Gelman, and their support of the Mexican art scene.

“Jacques made his fortune when he arrived in Mexico City through the burgeoning film industry from 1941 and his discovery of the comic actor Catinflas,” says van Raay.

“He came from Russia, while his wife was Czech. They started collecting art in 1943. Their collection is now the most important private holding of Mexican modern and contemporary art.”

As well as Kahlo and Rivera, their collection of Mexican art includes works by Siqueiros, Jose Clemente Orozco, Rufino Tamayo, Francisco Toledo and Leonora Carrington whose work has previously appeared at Pallant House.

On Natasha’s death in 1998 their collection of modern works by European 20th-century artists including Picasso, Dalí and Matisse was bequeathed to New York’s Metropolitan Museum Of Art.

But their Mexican collection was kept by the Vergel Foundation under the express instruction it should never be sold or put on a long loan outside Mexico.

With reports in 2008 from the New York Times that the Gelman collection had been removed from the museum in Cuernavaca over a dispute concerning the collection’s rightful ownership, it seems amazing that the work is here at all – let alone in Chichester, having travelled there via Istanbul and Dublin.

“People have to come down to Chichester to see it,” says van Raay.

“We never share an exhibition with London."

* Open from 10am Tues to Sat, 11am Sun, entry to exhibition £2.75 on top of regular admission, entry to gallery free on Thursdays 5pm to 8pm, half-price Tuesdays, £8.25 all other times. Call 01243 774557.