Trains are now back up and running between Didcot Parkway and Swindon.
A replacement bus service had been in place until 12.50pm after a body, believed to be that of a woman, was found on the line near Swindon.
Network Rail have warned that there may still be some delays and cancellations in order to get the best possible service for peak time.
A spokesman for British Transport Police said: “Enquiries are ongoing to establish the person's identity and the full circumstances surrounding the incident, including how the body came to be on the tracks.
“Anyone with any information about the incident should contact BTP on Freefone 0800 40 50 40 quoting reference number 200 of 16/12/2011.”
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