When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
The "chrome" window trims on the XF are in fact anodised aluminium, and I suspect they are the same for the XJ.
These trims commonly suffer from a tarnished look, mine does, and nothing but nothing I have tried makes any difference, including Autosol Chrome Polish, Autosol Metal Polish and Autosol Anodised Aluminium Polish.
Most "chrome" on cars these days is covered with a layer of clear plastic. So polishing with Autosol doesn't touch the metal at all. On some parts, over time, damp creeps behind the clear plastic and dulls the shine. However use of metal polish is ineffective because of this plastic layer. There really isn't a lot one can do about this.
Certain parts can be anodised aluminium, but are sometimes stainless steel. These are normally not covered with a plastic layer.
I have a tube of Autosol in the garage, but find I mainly use it on my MG Midget, which still has a lot of traditional chrome-plated Mazak parts.
The only test is to try a bit of Autosol on the part and see if it does anything at all. If it doesn't you have that plastic layer. Virtually all anodised aluminium is a matt finish as the anodising is done using an electrolyte bath and electricity. It's a reverse of plating, basically.