Even cutting back by swapping cow's milk for oat milk in your coffee could increase the risk of iodine deficiency – potentially causing weight gain, memory problems and chronic fatigue.
Children, adolescents and pregnant women face the biggest risks, British researchers writing in The Lancet Planetary Health journal said.
This is because iodine is essential for the production of thyroid hormones that help regulate metabolism and support normal growth and brain development.
Without enough iodine, the thyroid can become underactive, slowing metabolism and making weight gain more likely, with some studies linking the condition to weight gains of up to 5kg.
Even mild deficiency during pregnancy can result in long-term cognitive impairment in children, research shows. Yet, around a third of women of childbearing age are low in the essential mineral.
Swapping to plant-based milks, yoghurts and cheeses can also lead to deficiencies in calcium, vitamin B12 and riboflavin – which helps keep the skin, eyes and nervous system healthy.
Experts from the University of Surrey and Queen's University Belfast studied the dietary intake of 3,500 people from the National Diet and Nutrition Survey.
After analysing the nutritional content of 164 non-dairy milks, 76 yoghurts and 67 cheese alternatives, they found only just 12 per cent were fortified with iodine.
While 61 per cent contained added calcium, just one in five were fortified with riboflavin and 46 per cent contained vitamin B12.
Even modest reductions in dairy consumption led to declines in all four micronutrients – with iodine seeing by far the steepest decline.
Researchers found that replacing 20 to 35 per cent of dairy products with plant-based alternatives significantly increased the number of women and girls failing to get enough iodine.
Among teenage girls, the proportion with inadequate iodine intake rose from just over half to almost two-thirds following the switch.
Among women of childbearing age, the percentage failing to get enough iodine increased from 32 per cent to 42 per cent.
If all dairy was replaced, iodine deficiency rates rose to a staggering 80 per cent among teenage girls, and 72 per cent among boys of the same age.
'The UK is particularly vulnerable to iodine insufficiency due to a lack of an iodine fortification policy such as universal salt iodisation, which many other countries have,; Dr Sarah Bath, the study's lead author said.
'But many people are unaware of the importance of iodine - and the fact that dairy products are one of its richest dietary sources in the UK.
Experts say it can take years for the condition to be diagnosed – with patients, who are usually women, still not being listened to when they go to the doctor, their symptoms are blamed on depression or menopause instead
'Unless fortified, plant-based alternatives contain very little iodine - and this could cause problems for some people.'
The study also found calcium intake would suffer if dairy products were removed from diets.
Around a third of teenage boys already fail to get enough calcium when eating a balanced diet.
Replacing dairy products with plant-based alternatives pushed that figure to almost half.
If teenage girls made the same dietary swap, 70 per cent of them would be classed as calcium deficient – putting them at risk of osteoporosis later in life.
The researchers concluded that mandatory fortification of plant-based alternatives with key nutrients could help protect public health.
They also suggested adding iodine to bread as a cheap and effective way to boost intake across the population.
Many countries already fortify salt with iodine to prevent wide-scale deficiency.
However, public health officials in the UK have been reluctant to follow suit because it conflicts with efforts to reduce salt consumption.
'Nutrition policy must evolve in tandem with environmental targets - however it is important that shifts towards more sustainable diets do not compromise on public health,' Dr Katie Nicol, research fellow and study co-author said.
'Fortification of foods is one way this could be better achieved. However Government policy is needed to make this happen.'
Dr Janette Walton added: 'With dietary guidelines now recommending a large shift away from animal-based diets to more plant-based diets in response to global substantiality goals, unintended consequences for the health of teenage girls and young women must be considered.'
Global nutrition experts not involved in the study welcomed the findings.
'This paper presented credible alternatives which largely but not completely alleviate the deficiencies that would otherwise occur,' Professor Keith Frayn from the University of Oxford said.
How to get more iodine in your diet – and the tell-tale signs you might be deficient
A low intake of iodine over a long period of time will put stress on the thyroid gland, which may be visible as a lump in the neck, the British Dietetic Association states.
Other common signs include fatigue, weight gain, dry skin, constipation, difficulty concentrating and hair loss.
NHS guidelines state that people should be able to get all the iodine they need by eating a varied diet that includes fish, eggs and milk.
However, for those who avoid animal products, experts say that a supplement may be necessary.
Some plant-based drinks – including products sold by Oatly and M&S's Plant Kitchen range – are fortified with iodine.
However, organic milk alternatives cannot legally be fortified. While soya milk naturally tends to be slightly higher in iodine than oat or almond alternatives, all three provide very little unless iodine has been added.
Experts also warn that more is not always better. Excessive iodine intake, particularly from seaweed and kelp supplements, can disrupt thyroid function and lead to symptoms including weight loss, tremors and confusion.