When you travel to Oxford, you may want to get the Airline Bus from Heathrow to Oxford. Very convenient and easy. Also, if you are traveling between London and Oxford, there are both trains from Oxford to London Paddington Station and buses from Oxford Gloucester Green bus station to several stops in London. Actually, just Google your “point A” to “point b” and you will get accurate and usable directions for buses, trains, subways, and various combinations thereof.
Regarding the cell phone, if ATT is requested to do so, they can unlock your iPhone so that it can be used with the appropriate sized SIM card from another carrier. Then you can buy SIM card in advance as I suggested, or pick one up during your upcoming visit at one of the brick and mortar stores in Oxford. They also have a SIM card store in the arrivals hall at Heathrow, but they will charge you for SIM cards which are given out for free at various cellular network stores in the UK.