The E-type had an early-staged prototype with 4 doors, as you can see below. It was probably one of the first 4-door coupes. This E-type sedan was developed further as the Jaguar XJ
The new F-type is seen as the successor of the E-type in some ways. So when I saw these E-type sedan prototypes, the decision for a rendering of the F-type sedan was made very fast. The wheelbase is made longer and the roof is higher and less sloping, which accommodate more head room for the rear passengers.