Samantha Kendall, 28, who weighs four-and-a-half stone, is said to be on the brink of death. Her identical twin, Michaela, died three weeks ago. The girls apparently developed the disease after making a slimming pact, aged 14, following taunts from friends.
At her Birmingham home yesterday, their mother Susie Kendall, 47, said she needed to raise money to send Samantha to a Canadian institute because specialists in Britain could do no more for her daughter.
Mrs Kendall said: 'Time is of the essence. Sam may not have much longer. Losing one daughter is bad enough - I couldn't bear it if I lost both of them.'
Last night anorexia experts in Britain were divided about the quality of treatment available at home. Dr Janet Treasure, head of the eating disorders clinic at the Maudsley Hospital, London, warned that there were no treatments available in Canada that were not available in Britain.
She said: 'The US and Canada base their treatments on those devised here. I am surprised . . . that the woman has not been referred to a unit like ours. We have patients coming in who weigh as little as she does and who gain weight.'
But Susie Orbach, a psychotherapist and author of Fat is a Feminist Issue, said that some Canadian centres provided more humane, forward-looking treatments than those available in Britain.
Dr Treasure claims anorexia has a genetic component. In a study of 80 sets of twins, she found identical twins were far more likely to share the condition than non-identical twins.
But Ms Orbach argues there is no genetic component to anorexia and that the causes are social and psychological.
Less than 1 per cent of the population suffers from anorexia - 90 per cent are young women. Dr Chris Fairburn, senior lecturer in psychiatry at Oxford University, said anorexia was confined to developed countries where thinness was highly prized. Middle- class girls were more likely to develop the disease than working-class girls, and having an unhappy childhood, perfectionist tendencies and low esteem all increased the chances of developing the illness.