Emergency services responded to reports from the railway line near Bristol Temple Meads earlier this afternoon.
Disruption is expected until 6.30pm.
A Great Western Railway spokesperson said: “Unfortunately, a person had been struck by a train, leading to all lines being blocked.
“It was necessary to bring all trains in the affected area to an immediate stop.
“We are now in a safe position to start operating trains on all lines into and out of Bristol Temple Meads. There will still be further delays due to the incident.
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“Train services running through this station may be cancelled, delayed by up to 45 minutes or revised.”
Anyone who was onboard one of the services at the time of the incident or who knows someone else who needs support can call Samaritans on 116 123 for free at any time.
Many football fans from Swindon are expected to be travelling by train to Cardiff for this evening’s away game, which is due to kick off at 7pm.