Assuming Mr X owned a UK residential property when he became an Australian tax resident.
According to ATO's website (How changing residency affects CGT), when you become an Australian resident for tax purposes (other than a temporary resident), you are taken to have acquired your CGT assets at the same time, for their market value at that time. This is sometimes called 'deemed acquisition'.
I take it that this market value becomes the first element of the UK residential property's cost base (Cost base of assets).
As for determining the second to fifth elements of the UK residential property's cost base, does Mr X also take into account those costs he incurred prior to him becoming an Australian tax resident, e.g. legal fee incurred when he originally purchased the UK residential property?