The permanent solution is likely to involve one of
- Cantilever sheet piles at the toe
- Precast concrete retaining wall sections at the toe
- Gabion walling at the toe and probably up part of the slope
- Widening the embankment with a shallower batter
Then the slipped material would need to be removed and replaced with free-draining granular fill, compacted in layers and keyed into the remaining embankment.
None of that is likely to be feasible in a few weeks, even if NR can invoke emergency powers to gain road access to the site. (Statutory undertakers like power networks can normally do so, but I don't know if NR have that authority).
I expect that it will be a two-track railway for several months, though I'd be happy to be proved wrong.
(Disclaimer: I have no knowledge of this particular site, but I've been involved in similar slope stabilisation works in a non-railway setting).