If you call in sick for more than three days you usually go through your own doctor, so that you get a certification that you're taking X days off in order to cure yourself
For long term absence each country has different rules and paperwork.
In theory you should get a sick note after 3 days, because the government pays SSP (statutory sick pay) if you're ill, but in practice most companies pay you at your normal salary rate (if you're permanent, not per hour) and don't bother asking for sick note as the SSP is little more than minimum wage. Of course, this is in tech, I know that there are a lot of crappier jobs where employers trust their staff less, and I suspect in those industries the sick note is very much required.