The promenade has been shut in Corton near Lowestoft in Suffolk because of fears the cliff may move after part of it slipped earlier this week.
The whole promenade will be closed from Bakers Score to Cliff House. Waveney District Council took the decision to close the area after heavy rain saturated the cliff face, making it unstable.
The council have asked engineers to assess the condition of the cliff.
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With the cold weather expected to last for at least the next five days, the Met Office has issued various snow and ice warnings.
Cold but dry and bright this afternoon followed by a risk of icy stretches tonight.