The following is on the official CW site - it bears up what I and others have said, so if contemplating the walk - take care!
StriderMORE LANDSLIPS ON CLEVELAND WAY

In the wake of the recent torrential rain it is estimated that up to 200 landslips have taken place along the coastal stretches of the 110-mile Cleveland Way National Trail. The North York Moors National Park has legally diverted the path in three badly affected locations and is urging walkers to take extreme care all the way along the coast.

Malcolm Hodgson, National Trails Officer for the Cleveland Way, said:

"There are numerous small slips along the coastal section of the Cleveland Way. The three diversions allow the route to remain open. Providing walkers exercise extreme caution no major problems should be encountered. However, we are suggesting that walkers might want to explore other, perhaps more suitable routes at this difficult time."

The three, signed diversions are:

Saltwick (just south of the Abbey in Whitby)
Runswick Bay - from Runswick Bank Top to just to the west of Kettleness (with the permission of Mulgrave Estates)
From Lebberston Cliff to the Blue Dolphin Holiday Park
Please contact Malcolm Hodgson on 01439 770657
(m.hodgson@northyorkmoors-npa.gov.uk) for detailed information on the diversion in place.