His first attempt was a failure. Using a breathable material that lets vapour out but keeps air in, he created a sealed pillowcase to cover the pillow. But when he tried to rest his head on it, his head bounced off; because the pillowcase did not let air out, it was like an inflated balloon.
To overcome this problem, he created a new version with internal air sacs built into the covering. When the sleeper's head touches the pillow, instead of bouncing off it displaces air into the air sacs at the sides, and promises a dust-mite-free night.
The pillow is made by the Sylvan Corporation, which Walker runs in Manchester, and business has been brisk since it went on sale earlier this year. Now it has won a place in the Millennium Dome exhibition of 200 products for the year 2000. It will be featured alongside a fabric normally used to make weatherproof outdoor wear which has been adapted for use by asthmatics. Pertex is made from continuous-filament polyamide fibres that are finer than human hair. They are densely woven, so they prevent penetration of the dust mites, and can be used as protective sheets covering mattresses.
The fineness of the weave means that Pertex, made by Perseverance Mills, Lancashire, provides a natural barrier against the mites without the need for additional chemicals - which can themselves trigger an allergic reaction.
Around 2 million house dust mites live in the average mattress, feeding on dust. Their droppings contain allergens that are believed to aggravate asthma, but there is uncertainty about whether reducing the mites eases the symptoms.
A spokesman for the National Asthma Campaign says: "There is a shortage of medical research to show whether reducing dust mites really helps. We recommend sufferers to try different materials, synthetic and natural, to see what works for them."
The Sylvan Corporation (01706 712925); Perseverance Mills (01282 778711). Marks & Spencer sells Pertex duvets (pounds 100-pounds 150), mattress-protectors (pounds 79- pounds 95) and pillows (pounds 37 for two)