I melted my car (with picture)! Help!

That looks like it! Thank you!

 

So I said I would report back... here you are with the final results!

It cost £68 (including VAT) for part number 58841-47050-C0 (RHD Shift Cover Plate Black). If you don't include the -C0 at the end of that code you will get a white RHD plate. There is an optional extra "Piano Black" plate available, but they quoted me £130 (around £156 with VAT) - optional extras cost a LOT more than "spare parts" that are completely identical.

The old cover removed quite easily. I used a plastic pry tool that I inserted via the big shift lever hole towards the clips. I did try prying up from the edge but my pry tool wouldn't get under the lip. It popped off without too much effort.

All of the buttons (EV Mode, Drive Mode, and P) are attached to the cover plate. The cables don't give you much slack... just enough to get the cover off over the shift lever. So be careful you don't pull the plate off too hard.

The EV Mode and Drive Mode buttons are grouped into a single holder. Both button holders are simply clipped into place into the plastic cover plate via some (4?) clips. I removed them by applying pressure from the button side while using a small flat screwdriver to push the plastic of the old cover plate outwards away from the switches on the other side.

Once that's done you're left with a removed cover plate, and two sets of switches hanging down by their cables.

Fitting the new cover plate was just the reverse of the process... It all just pushed together really easily and simply.

I personally thing the Piano Black looks better than the white, given everything else in the car (apart from a couple of plastic bits on the steering wheel) is black.

Pictures are below. The old damaged white cover plate is at the bottom of the pictures. You can see the orange clips that hold it in place on one, and the damage on the other.

Huge thanks to all that helped, especially Electroingenieur for the part number. That saved me a lot of cash!

 

You might be able to get it as a factory install when ordering the car, but what I was quoted is for a self-install. When I log in to my Toyota UK account online, and click on the page that shows what accessories / optional extras are available for my car, it shows the usual roof racks, roof boxes, boot liners, etc, and one of them is the black cover! If you add that to your basket it's the same cost as what I was quoted by the parts department.