Yorkshire is expected to see flurries of snow, especially on the coast, towards the end of this week.
Forecasters said plummeting temperatures could bring the snow showers to many eastern parts.
The Met Office says the weather will change from Wednesday, with colder temperatures spreading from the east, accompanied by the chance of wintry showers.
Night-time temperatures are already low with areas of Yorkshire getting down to the minus 5C mark overnight from Sunday to Monday.
Emma Sharples, from the Met Office, said temperatures are likely to dip by at least two or three degrees by Thursday for much of England with day time maximums unlikely to rise higher than around 5C (41F).
Ms Sharples said: “We’ll definitely be seeing low single figures by the end of the week.
“And, of course, overnight, where skies remain clear and away from coastal areas, we’ll see temperatures dipping down to negative figures
“The wind will start to pick up from the east, so it’s not just numerically temperatures being low but, also, the wind chill’s going to add to that as well.”
She said the colder temperatures could be accompanied by the odd wintry flurry, mostly in the east.
The Met Office is not currently expecting these to be significant snow falls.
“There will be some snow around,” Ms Sharples said.
“It looks like there will be some wintry flurries down the east coast on Thursday, Friday and into Saturday.
“It’s difficult at the moment to say exactly where we’ll see those but it’s definitely turning cold enough.”
Ms Sharples said the colder weather will come as air from the freezing continent moves over the UK once the latest weather front from the Atlantic moves off.
She said on Monday: “Once we get through this spell of rain today most places will be mostly dry, so that’s a good thing.”
The yellow warning issued for Northern Ireland and parts of western Scotland by the Met Office was in response to high winds expected from Monday afternoon.
The statement said gusts of 50-60 mph are expected across the affected area with with isolated gusts of 65 mph in the north of Northern Ireland.
It said gusts of up to 75mph are likely in exposed coastal parts of the Western Isles.
The Met Office said: “Some disruption is possible to road, air and ferry transport, whilst localised power interruptions are possible.”