A distinction in the overall course would enhance your chances of getting an offer from Oxbridge. If not, you should try to get 70 or more on your dissertation. Also, don't forget the really key piece of document is your RESEARCH PROPOSAL. If you cannot demonstrate passion, interest, familiarity with relevant literature and potential contribution of your proposed study, the chances of getting an offer is close to nil.

Hello Alex (future PhD student) I am curious which country are you talking about where its local master degree is considered equivalent to the PhD in 'western countries'? What about the PhD degree in your country, is there an equivalent degree in the western country?

At Cambridge University.