You know you could always ignore the UK earnings as an option - at the risk of a possible tax audit by IRD. Despite the chances are pretty low, the IRD has little ability overseas to find out your earnings. Perhaps more ability in the form of land property transactions as conveying lawyers are required to record and submit directly to the tax dept.
But if you want to go strictly by the books, all you have to do is declare the 5 months UK earnings under the "Foreign Tax" section of the IRD tax return.