As you have found out, the paint on trailer wheels is very thin and does little to prevent rusting.
Some wax polish may delay the inevitable.
This leaves you with the choice of respraying with primer and top coat or use something like Hammerite or chassis paint.
Rounding of any sharp edges on the rim will help the paint adhere for longer.
This time, effort and cost must be related to the cost of a new rim at £10.
I am not aware of a supplier of galvanized rims in the UK.