Alan Lockwood, 41, from Horbury, Wakefield, was seriously injured in a crash which happened close to the McDonald's outlet at about 8.40am on Tuesday, September 29.
Mr Lockwood was a passenger in a blue Chevrolet Spark which crashed with a blue Ford Eco Sport.
He was taken to hospital but died of his injuries on Thursday, October 1.
Officers are now appealing for any witnesses to the crash or anyone with dash cam footage to contact them.
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They would also like to speak to the occupants of another car which is believed to have been involved.
The only information known about this car is that there were two women inside.
Anyone who witnessed the collision, or anyone with dash cam footage of the vehicles prior to it is asked to contact the Eastern Roads Policing Unit on 101 or by using the options on the West Yorkshire Police website, referencing log 309 of 29 September.