The products on average contained two per cent of the iodine found in cows' milk, the British Journal of Nutrition reports.
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Iodine is required to make thyroid hormones, which help keep cells and the metabolic rate healthy. It is especially important for the brain development of babies, particularly while they are in the womb.
Professor Margaret Rayman, an expert in nutritional medicine at the University of Surrey, said: "Many people are unaware of the need for this vital dietary mineral and it is important that people who consume milk-alternative drinks realise that they will not be replacing the iodine from cows' milk which is the main UK source of iodine.
"This is particularly important for pregnant women." Dietitian Dr Sarah Bath, lecturer in public health nutrition at Surrey, added: "If avoiding milk and dairy products, consumers need to ensure that they have iodine from other dietary sources, where possible."
Of the drinks tested 14 were soy, 11 almond, six coconut, six oat, five rice, three hazelnut and two hemp. They were each compared to semi-skimmed milk.
Earlier this year the UK's National Osteoporosis Society warned of the clean-eating fad after finding that more than a fifth of young adults had severely cut their milk intake.