Rhymney Valley train services will be terminating at Bargoed for the rest of the day. Replacement buses will operate between Bargoed and Rhymney.
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David and Angela Southwood, from Newport, say they plan to live in a caravan over the border after learning of the decision.
The fog is expected to become quite widespread and locally dense and freezing during the evening
A hospital has accepted liability for the death of a two-year-old boy who waited more than nine months for a key medical assessment.