Other non-food items she devours include sand and chips of cement from paving blocks.
Jessica suffers from Pica syndrome, a rare medical disorder that leads to an appetite for non-nutritious substances. It is more commonly recognised among pregnant women, some of whom develop unusual cravings.
"I was really shocked when I realised just how much she was eating. If you lift up the carpet in her room now you can see there is no underlay left," her mum Kelly Knight, said.
"'We are at our wits' end. We try to keep her busy so she doesn't do it, but if we try to stop her she will find a way to do it.
"I'd have to remove everything from my house, including all chairs and sofas."
Ms Knight, 36, first noticed the problem when Jessica was two and began eating the filling from a children's armchair.
Staff at her pre-school also spotted her licking her hands and placing them in a sandpit before sucking the grains from her fingers, before tell-tale signs of snack-attacks became clear from the damage to items around the house.
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Jessica, who has a three-year-old sister, Jennifer, is now allowed to keep a small purse filled with some of the spongy underlay to eat.
"We'd rather she ate the underlay because it is non-toxic. If we try and stop her we fear she will eat something with chemicals in it," Ms Knight said.
Experts have examined Jessica but said they cannot intervene until she is six, and old enough to make conscious decisions about what she eats rather than acting on impulse.
Fortunately, she does like plain sausages, cheese strings, rice pudding, bread, Weetabix and fish fingers.
But her unusual snacks can leave her in agony because they cause stomach cramps and constipation.
Despite her age, Jessica is aware that her diet is unusual, and does worry what people think. She also shuts her little sister out of their shared room when she is satisfying one of her cravings, saying: "I don't want her to be poorly."
The family will find out this month if Jessica is on the autistic spectrum, which is often linked to Pica.
The Challenging Behaviour Foundation, a learning problems charity, said: "It is estimated that four to 26 per cent of people with learning disabilities display pica behaviour.
"Whilst some objects pass through the body without harm, pica can potentially be life-threatening. Risks include vomiting, blockages, choking and poisoning."
Dr Alison Sansome, clinical director at Cambridgeshire Community Services NHS Trust, added: "Pica is a complex condition and treatment is dictated by the specific circumstances in each case."
What is Pica?
Pica is an eating disorder that is characterised by the desire to eat items with little or no nutritional value.
These can include stones, sand, paint and dirt.
It is most common in people with learning disabilities and during pregnancy.
It can cause a range of serious complications if the person is eating something that is poisonous or indigestible.
These include being poisoned by toxic ingredients and having a part of the body obstructed (which is often seen in people who eat hair).
It can also lead to excessive calorie intake, but also nutritional deprivation if the person eats a substance with no nutritional value instead of nutritious foods.
The person can also damage their teeth and be infected with parasites.
