Work to clear thousands of tonnes of earth and rock which have blocked a deep railway cutting at Harbury should be cleared by April 2 – Maundy Thursday – and services from Leamington to London resumed, said Network Rail.
The landslip by the 73-yard Harbury tunnel involved 350,000 tonnes slipping towards the cutting.
More than 100,000 tonnes has been removed and sophisticated monitoring equipment installed to track the continuing movement of the slip.
More than 50 freight trains and 80 passenger trains use the line daily.
The landslip on January 31 caused massive disruption, with people forced to use the West Coast Mainline route to London or buses to Banbury to rejoin the Chiltern Line.
It has also caused major problems on CrossCountry services from the North to the South Coast via Birmingham.
Transport Secretary Patrick McLoughlin visited the site and said: “I regret rail passengers are being inconvenienced by this serious landslip.
“Network Rail engineers are working to resolve this situation, and train operators have told me they are doing everything possible to give passengers up-to-date information and to keep them moving. My officials are closely monitoring the situation and will offer whatever support is required.”
Network Rail chief executive Mark Carne said: “Passengers can be assured that we are using all available resources, and working around the clock to reopen this railway safely.
“This cutting has suffered from landslips since it was built and we are looking at what new engineering solutions are available to make it safer and less at risk to landslips in the future.”
When the landslide happened Network Rail was carrying out stabilisation work after a smaller landslip on the site on February 14 last year.