The test, called EarlyCDT-Lung, will include 10,000 high-risk smokers (defined as having smoked the equivalent of 20 cigarettes per day for over 20 years).
It detects signals produced by the immune system when lung cancer is present.
This can mean up to five years earlier than tumour detection.
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Transport Secretary Chris Grayling believes Network Rail should share the responsibility with private train operating companies.
Two vehicles were swallowed up by the sinkhole on Sunday night, killing Dora Linda Nishihara and injuring one man.
Elliott Livingstone, aged three, spent most of his life in hospital before the operation in April.