Last Saturday, Mrs Gough-Irwin underwent an operation to have the top of the bitten finger amputated, but her condition deteriorated when she began "hallucinating" and was "confused", according to her family.
She died in hospital on Friday.
Julie Lungley, 43, one of Mrs Gough-Irwin's four daughters, said her mother's death has left her "numb and in total shock".
Staff at the hospital have since confirmed to the newspaper that they are investigating whether the bite caused Mrs Gough-Irwin's death, and her family will be meeting with hospital managers.
If the creature was the cause, she will become the first known person to have died in the UK as a result of a spider bite.
Related to the deadly black widow spider, 10p-sized false widows leave their victims with painful bites which can become swollen. While some people have reported becoming unconscious after encounters with false widows, no deaths have ever been confirmed.
Most false widows have bulbous bodies with white markings, and are native to the UK and are therefore common site in the home, particularly in the autumn months. But the noble false widow - the most poisonous in the UK - was imported from fruit crates from the Canary Islands around a century ago and has spread from the South Coast.
Dr Tim Cockerill, a presenter on BBC's Spider House, told the newspaper that the noble false widow is nowhere near as poisonous as the black widow, and its bite is akin to a bee sting.
He added that in most cases, when people die of insect bites it is due to a bacterial infection rather than venom.
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