Just to let you guys know - I have a 1995 XJ6 which I'm in the process of giving a light renovation and succeeded in removing the rear bumper without the captive nuts turning.

My approach was to drill a hole bigger and bigger in the centre chrome strip. I used masking tape lined up with the two bolt heads near the exhaust tips. I then extended the tape up and over to the bumper top. Once I'd drilled a hole with the biggest drill bit I had to hand, I used a mini bolt cutter to tear the chrome until saw the other threaded side of each of the two bolts. (Sadly this sacrifices the chrome strip, but it needed replacing anyway).

Over the last week I have kept visiting the car to saturate the bolt threads and captive nuts with Plus Gas, 3 in One oil and WD40, using the hole I made to access the bolt from other side.

On trying today, the driver's side bolt undid without drama. The kerb side bolt was a lite harder to undo so I sprayed more PlusGas whilst turning (carefully!). Note: You will always be turning the socket CLOCKWISE if you are looking from a top down perspective!

The exhaust tips removed by drilling the allen screws. I had to spray plenty of WD40 into the space between the exhaust pipe and the trim. Twisting left to right and towards yourself on the tips should have them removed in minutes.

Cheers!

 

If you undo the bumper mounts from the inside of the boot (four nuts each side) you can withdraw the bumper from the car. Once the complete bumper is removed you can access the hardware holding the chrome strips on and get to the seized bolts.

 

That's a less wasteful solution, yes. However if it's difficult to undo those I recommend my method.