20/50 is too thick when cold for the UK, you need 10/40 or 15/40. Try Tesco, the diesel mineral oil is exactly the correct spec for the old SOHC Hondas.
Blue smoke is never normal for a Honda 4 stroke and would be either valve guide wear/ stem seals or bad piston/rings but possibly excess crankcase pressure if a breather is blocked although that usually blows seals and/or gaskets first