Dr David Kirrage from Public Health England says the risk that any child has caught an infection is "negligible", and they and Moreton School in Wolverhampton are working to reassure parents, after 20 pupils were jabbed with a diabetic testing needle.
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Further snow showers are expected to continue through the morning, easing somewhat during the afternoon.
Strong, bitterly cold winds, with sunny intervals and scattered snow showers.
Old Market Square in Nottingham was a blaze of orange, green and white as hundreds brave the blizzard-like conditions.