The warning has been put in place from Tuesday at 9am until 6am on Wednesday.
A spokesperson for the Met Office said: "Heavy showers and thunderstorms are expected to develop during Tuesday across much of Wales, northern and central England.
"These will last well into the night across north Wales and north-west England in particular where they could be prolonged in places. 20 to 30 mm of rain is possible in around one or two hours, and a few places could see around 60 mm in three to six hours.
"Lightning and hail may pose additional hazards in a few locations."
What to expect according to the Met Office
In Wakefield and the Five Towns, rain is expected to begin at around 3pm on Tuesday, continuing into the evening.
Heavy cloud with outbreaks of rain are then expected into the early hours.
Wednesday will see a mixture of sunshine and showers across the Wakefield district, with the poor weather likely to continue into Thursday and Friday before a cool and cloudy weekend.
Spray and sudden flooding could lead to difficult driving conditions and possibly some road closures
Where flooding or lightning strikes occur, there is a chance of delays and some cancellations to train and bus services
There is a small chance that homes and businesses could be flooded quickly, with damage to some buildings from floodwater or lightning strikes.