The front and rear bumpers on the Series II E-types are pretty easy to refit. This is in contrast to the rear bumper on the Series I which requires removal of the gas tank.  All of the attachment bolts are accessible and can be inserted and tightened from under the car.  The rear bumper is a three piece

Jaguar E-type Bumper Installation

section that bolts together and bolt to the body. There is play in the connections that allow fine fitting to get the gaps right. I found it easiest to fit the bumper rear bumper loosely on the car and make sure the gaps were correct before tightening the bolts that hold the three pieces together.  Both the rear and front bumpers take some fiddling to get the fit right. It is wise to protect the body with thick tape near where the bumper fits to avoid gouges and scratches.