Professor Williams is based at Queen's Medical Centre
Dawn and Mark Longden have two children who suffer so badly from the itchy skin complaint that they sometimes have to have their hands wrapped in bandages.
But since they installed a water softener in their Melton Mowbray home three years ago, Mr and Mrs Longden have noticed a marked improvement for nine-year-old James and his seven-year-old sister Emily.
They installed the device at the suggestion of Professor Hywel Williams from Queen's Medical Centre in Nottingham, whose research had shown that hard water may worsen the condition.
Bee stings
Mr Longden told the BBC: "Their eczema affects their whole life, from getting up in the morning until late at night and also through the night."
Emily said: "It feels like you're being stung everywhere by a bee."
But now, since the installation of the £600 water softener, the children's eczema has been a lot more controllable.
Professor Williams said the findings showed the need for more research.
"We need to really establish this with a proper study.
"Many patients moving from hard to soft water areas report an improvement in their eczema.
"But the study we did doesn't really prove that buying a water softener helps eczema - we need to do a proper randomised study to investigate that."