Clifford, the 6.00x16 Dunlop Roadspeed did come on the XK120 from the factory. I had one in the boot of my car when I acquired it in the early 60s.There are several vendors (Coker comes to mind) that offer 6.00x16 wide whitewalls albeit not Dunlops. I recommend you try an internet search.
If you intend to drive the car regularly, I highly recommend changing over to radial ply tires. They are also available in wide whitewall...at a price. I believe Vredestein offers a tire that will work with the 120.
Good Luck!