I don't know if access from the beach is possible to bring materials in.
It may be possible to bring in rock protection at high tide in bottom dump barges and then send in D9's, back-hoes and Moxys at low tide to bring the rocks up the beach to form a first line of defence. I was involved in a similar operation along the North Wales coast.
This one is a difficult job because two faces need to be protected, the seaward to support and protect the railway, and the landward to support the properties and ground above the railway.
Unfortunately, the situation can't be fully assessed until the storms abate and a full inspection of the line, the condition of the adjacent properties, and any unsupported ground above the line can be carried out.
The rock protection could start fairly quickly to stave off the future onslaught of the waves, when there's a weather window which allows it.
It's a wonderful section of the UK's railway network.
Good old Isambard Kingdom B.