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I have travelled and lived in both London and Oxford. I found the easiest and the cheapest (they have concession rates) method of transport between the two cities was by coach. There is the Oxford Express and the Oxford Tube. They are much more regular (every 10 mins in the day) and both run 24 hours (less regularly) so you don’t need to plan your trip there and back. Another bonus is they stop at a number of different places in Oxford and London so you can get closer to your destination.