How much the previous university's prestige matters for a phd enrollment? I'd like to apply for a PhD in Ancient History at Oxford in the future. 
Currently I'm planning to apply for a ResMa in Ancient History at Leiden university, in the Netherlands, which is thaught in English. 
Is it a recognised uni for classics in UK or the US or should I do a British university instead, such as Durham, Mancester, UCL, St Andrews and so on to have better possibilities to be taken at Oxford? 
Thank you all!
All of the universities you have mentioned are top-league universities with high prestige. As for whether you have a better chance of getting into Durham, UCL etc versus Oxford is debatable. They are internationally renowned and the competition very high. Of course, Oxford is Oxford, but there's little point in going to Oxford just because it's Oxford, which it sounds like you want to do, because you don't seem to know what it's like for your specialist subject area. 

The most important thing about any university is the staff in the departments, not necessarily the university itself. These are the supervisors who you will be learning from and have constant contact with. Their tuition can be either inspiring or a hindrance to positive learning. 

All of the universities you mention are good. Take some time to visit their websites, look at the department members, their publications and what feel you get from the institution and the department. Do you get the impression that you really like the place? Does it look inspiring? Does it make you want to find out more, do you think you that when the course gets difficult [not if] you would be able to overcome the obstacles with the staff's support?

At the end of the day, finding out the answers to these questions is far more important that going to Institution A or B based on some arbitrary popular notion of league places. A slightly lower-league university may get a lot more out of you than one a few more places up depending on how well you gel with the department. If, after your research, you still want to go to Oxford and it looks right to you, by all means go for it, but don't get hung up on it. The amount that an institution inspires you will govern how much 'better' the 'possibilities' are for your entry.