Smart Casual Lab Clothes

Hi there, I am starting a degree apprenticeship as a trainee biomedical scientist at the end of September and as I am freshly out of sixth form, I just wanted some advice on what to wear on the days I go into work. I am going to be working in London in a lab that has both private and NHS samples if that changes anything. They said 'smart casual but with hair tied back and close topped shoes'. What is smart casual? I know it's stupid but everywhere seems to have different definitions like are jeans allowed? I have bought a pair of brown adidas spezials to wear as I thought they would be comfy if I am on my feet a lot. Any other advice would be great! Thanks.