The jumbo shrimp I get here are big, but not that big
, and they come shell-on, with a slice down the back and the vein already removed. I would never cook them with the vein in.
I rinse them under cold running water and run my thumb down the back to make sure all of the vein is out, mix them with olive oil and garlic and roast them shell on at 400F (don't know what the equivalent is in the UK). They'll turn bright red - I would guess at that size it would take about 15 minutes total, turning once.
You'll get varying opinions here about cooking them shell on or off
, I think it adds to the flavor and helps keep them from drying out if the shell is left on. Some of the meat will be forced out the shell during cooking, you can see enough of the meat if they are done or not without cutting into them. They don't take long.