A yellow weather warning for ice has been put in place for the region from 6pm tonight (Sunday) until 8am tomorrow (Monday).
The agency said: "Icy patches are likely to form on Sunday night and last into Monday morning.
"With surfaces left wet, from Sunday afternoon's mix of rain, sleet and snow, icy patches are likely to form overnight and into Monday morning on any untreated roads, pavements and cycle paths.
"Some injuries from slips and falls on icy surfaces are possible."
It said an area of snow was likely to move eastwards across many central and northern parts of the UK on Sunday.
The snow was more likely to affect higher routes with lower levels only affected more locally.