Stratford to Oxford by train: Take Chiltern Railways service to Banbury then Cross-Country or First Great Western train to Oxford. You may get a cheaper fare with an advance booking, but it is not necessary to book ahead.
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Oxford to Cambridge - best way is the X5 coach (bus) as the rail route involves crossing London by Underground. Coaches run every 30 minutes, journey time is 3 hours and there is no need to book in advance, just pay the driver (cash - fare is currently £11.40).
"There is also a bus route Stratford to Oxford"
There isn't, except on Sundays, and except for one long distance coach a day operated by National Express, not Stagecoach (leaves Stratford 1600, arr Oxford 1710). The weekday service advertised by Stagecoach involves changing buses at Chipping Norton: it's a tight connection and the connecting bus won't wait if your bus is delayed by traffic (quite probable).
Trains are, by British standards, infrequent (every two hours, roughly), but the service via Banbury is about 80-90 minutes.
Thanks dzug - I didn't know there were advance fares on the X5. I presume these have to be booked via the Megabus.com website though as they don't appear on the X5 one.
Answering my own question - yes you do book through the Megabus.com website. There is also a 50p booking fee on each transaction. Still £1.50 is a lot cheaper than £11.40 .....
Er - flanneruk - all those details you mentioned about the Oxford /Stratford buses were on the link I posted - except this "service" does actually also run at the weekend! :-)
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