Bit of a complex question.
HepatitIs is inflammation of the liver. Currently there are at least 5 forms described (lettered A to E). Hepatitis B is a highly contagious viral disease which can cause liver failure. It is also, to some extent treatable and you can be vaccinated against it. Your flying status will probably depend on your body's response to the virus. I do not have the details to hand but...
Acute infection would probably be a bar until it had settled down.
Complete 'cure' should mean that no further damage is expected and the patient is no longer an infection risk. Whether being an infection risk would affect your eligibility for a licence I don't know.
Chronic Carrier status is associated with an increased incidence of liver problems in the future which may preclude flying.
In summary, I would think that in most cases Hep B would not be a problem (unless flying with an infectious disease which is spread by blood and body fluids but not by contact or sneezing is forbidden). In a few cases there may be restrictions placed on licensing.
The CAA should be able to advise further