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Police said it was expected post-mortem examinations would be carried out on Sunday.
All rail services on the West Coast Mainline between Rugby and Stafford remained suspended.
A Network Rail spokesman said engineers had been unable to get onto the site because of the investigation, but were hoping to start work on Saturday afternoon.
"It's probably about a day's work and we hope to finish by Sunday evening. It should be clear for Monday morning commuters," he said.
There will be a reduced service and delays of up to 60 minutes on Virgin Trains services between London and north-west England which are being diverted via Coventry and will not call at stations between Nuneaton and Stafford.
On local services run by London Midland there is a replacement bus service calling at stations between Stafford and Rugby, with up to an extra hour added to journey times.
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