If your course is longer than 6 months (and your visa is valid for more than 6 months), then you are eligible to use the NHS from the moment you arrive in the country on your student visa.
It's not so much about being 'covered' as such, as it is not insurance, it just means that you can get medical treatment free of charge from the NHS (the NHS is a national service that is provided to the general public by the government and is paid for using public taxes, just like childhood education or the police and fire services). If you were on a course/visa that lasted less than 6 months, then you could still use the NHS, but you would have to pay for your treatment instead of getting it 'free' (so you would probably want to get travel/medical insurance to cover you).