Alexandra and her younger sister Veronica grew up in South Kensington. There were weekends in Sussex at the country cottage, where guests included Graham Greene, Anthony Quayle and the children's godparents, Charlie Chaplin and Ralph Richardson.
Yet all this was overshadowed by the knowledge that Alexandra had a life- threatening illness for which there was no cure. Last year, aged 43, she died.
Alexandra was nine months old when, in 1960, she was diagnosed with Diamond Blackfan Anaemia (DBA), an extremely rare form of anaemia caused by a congenital failure of the bone marrow to produce red blood cells. Hers was the first case the Great Ormond Street Hospital had come across, and it was the first to be documented in Britain. DBA remains extremely rare - on average, six children are born with it each year in the UK .
This made it much harder for her mother Joan, says Veronica, 39. "She had no idea what to expect when Alexandra was diagnosed, and treatments had not been much tried. My sister had a pretty unpleasant time of injections, transfusions and one drug that nearly killed her, as well as having her growth stunted.
"She wrote in her diary, `I put on weight and did not grow normally, so I looked like a dumpling and had the smallest feet of anyone in my class.' My mother was wonderful at keeping her worry to herself, wanting us both to have as normal a childhood as possible, but I know now how hard it was for her."
The exact cause of DBA is unclear, but it seems to be caused by a fault in one of the early stages of red blood cell production. A baby may be born well, but then fail to go on making the vital cells. In up to a quarter of children there is a fault with a gene (RPS19) and a hereditary link.
The symptoms are similar to other kinds of anaemia: pallor, irregular heartbeat, extreme fatigue and heart murmurs due to the increased work the heart needs to do to keep oxygen moving around the body. They are usually pronounced enough for parents to realise that something is wrong, so it is diagnosed very early, although some children develop DBA later.
This is how it was for Natalie Barb and Stuart Graham. Their first child, Saskia, three, was born normal but after that she did not make more red blood cells. Natalie says: "She got paler and paler. She was sleeping more than usual for her age and not feeding properly. When we took her to the doctor, they discovered that she had a haemoglobin level of 2.8, and 14 is normal. We were told it was DBA, but neither of us knew anything about it. We were reeling from the shock."
Diagnosis is easier if there is already an affected child in the family, or the baby has physical features of DBA, as about half do. These include an extra thumb joint, and characteristic facial appearance such as very wide-set eyes and a broad flat nose, but these may only be identifiable when a child is older. Otherwise, the disease is ascertained with tests to show whether too few red blood cells are being produced, and a bone marrow sample .
The treatment is basically the same as it always has been: steroid therapy and regular blood transfusions, both of which may have to be continued through life. Neither is a cure.
Dr Sarah Ball, reader and honorary consultant in paediatric haematology at St George's Hospital Medical School, explains: "About two-thirds of DBA patients respond to steroids, but because they have significant side effects - stunting of growth, bone weakening, diabetes, glaucoma and high blood pressure - we tend to put a strict upper limit on the dose. If this means the dose cannot sustain red cell count, or if the DBA does not respond to steroids, regular blood transfusions must be given."
The trouble here is that while normally the body absorbs iron easily and recycles it, with transfusions this does not happen and the iron gets deposited in the liver, heart, muscle, pancreas and elsewhere. Without treatment for this, the DBA sufferer is likely to die sometime around the teen years. To deal with the iron, chelation drugs are given, usually intravenously.
Veronica remembers the pattern of her sister's daily steroid injections, the visits to hospital for transfusions, and how Alexandra hated it all. She also remembers, with a wry smile, "sometimes feeling jealous of her when she got home from hospital and was allowed into our parents' bed. I knew I was the one with the lucky deck of cards, and that I shouldn't feel that way, but I did." And she says, smiling, that she suspects Alexandra knew she had a certain power with her affliction: "She admitted when we got older that she had bullied me a bit. She did things like telling me to kiss her toes if I wanted to borrow the Sellotape."
Natalie and Stuart know they have to be careful that their younger daughter Alice, 20 months old, doesn't feel jealous of Saskia, who inevitably gets a great deal of attention. But so far their main concern is helping their "stoic and defiantly happy" little girl cope with her monthly blood transfusions and the nightly infusion of chelating drug. Natalie says: "We have to persuade her to let us put the needle into a fleshy part of her body, and sometimes she really doesn't want that. Then it is left in for the night so the liquid can go into her. But we don't know if there will be side effects. So it's a difficult lifestyle for all of us. We cope, and just hope that there will be medical advances to make things easier in the future. What else can we do? But sometimes we both just cry."
The one way DBA can be cured is with bone marrow transplants, but the risk of this is unacceptably high unless there is a match within the family; then the success rate is 85 per cent. But, Ball explains, there is ongoing research into new drugs and treatments, and studies designed to learn more about the illness are under way.
Alexandra had a "fierce determination to live her life," recalls Veronica. They became ever closer as they grew older. Veronica remembers trips on the Eurostar to Paris and Bruges: "We always went first class, which she loved."
And she remembers with pleasure how Alexandra's godfather Ralph Richardson took an interest: "He used to visit often and he spent a lot of time talking with her, which she loved. Sometimes he'd perform. I remember one time he pretended to be a porter taking ladies' coats and stroking them, and he would arrive with gifts. I think he understood that she needed something special."
It was determination that enabled Alexandra to get over difficult schooldays when, as a result of missing so much time, she fell behind. And she also struggled with being profoundly hard of hearing. Yet she got into St Martins College of Art and then, with a Royal Society of Arts Bursary, into Chelsea College of Art. Life improved further when she met and married Andrew Gammon at the age of 28. They bought a house in Barnes, where they had a dog and two cats.
Unsurprisingly, there were further trials. At 32, Alexandra began to suffer depression, which she said "took hold of me like bindweed". Over the next four years she became agoraphobic and took up smoking, and then attempted suicide. In the midst of all this, she painted and created; Veronica remembers, during a period when she was "frustrated and angry", huge sculptures depicting injections, pills, needles - the elements of her disease. Then came a happier, more serene, time, when "the pictures were joyous, energetic and full of life".
These works are now being exhibited by the charity Paintings in Hospitals to open their new gallery. "Alexandra would have been so delighted by this recognition, and that makes me and our mother happy," Veronica says. A memorial award in Alexandra's name will also be launched to support one artist each year to create work to be hung in hospitals. This will be presented by the Max Reinhardt Charitable Trust, which was set up by her father early in Alexandra's life to fund research into DBA and to set up the national registry of children with the ailment to learn more about its cause.
For Alexandra, life ended quite suddenly. During her last year, her blood count had been dropping alarmingly. Although she rallied, she developed a haematoma, which became infected, and after a Christmas at which Veronica remembers that "she was fun and happy and seemed quite carefree," she died on 4 January at St George's Hospital in south London.
"It was a tragedy that my sister had this terrible illness," Veronica says. "But her art brought her pleasure and satisfaction; it mattered enormously to her, so she would be thrilled at the idea of this exhibition and bursary. She always said there should be more art in hospitals, and now there will be."
The Alexandra Reinhardt Exhibition is at the Menier Chocolate Factory, Southwark, London SE1 (020-7403 5893), to 25 February. The Diamond Blackfan Anaemia Support Group can be reached at 01246 828194, or www.diamondblackfan.org.uk. Contact a Family is an information resource offering support and contacts to families with a shared illness (020-7608 8702; www.cafamily.org.uk)