In Visual Studio Code Ctrl+V is not working on editor.
However from the command palette Ctrl+Shift+V is working.
@WebD'is answer is very helpful and I have upvoted it. But my comment focused on whether there was a conflicting binding for CTRL-V and how to find it. You can literally type "Ctrl+V" (note the "plus+" sign, not a hyphen) and it will find all keybindings that use that binding in whole or part. I suggest that there must be a something else also bound to CTRL-V.
Since this original answer, vscode introduced another way to see what other commands might be bound to given keystrokes. With the Gear/Keyboard Shortcuts file open click on the little keyboardy icon to the right (or Alt+K with this file open) and it will indicate Recording Keys next to it. Now you can literally press Ctrl+V (or whichever keybinding you are interested in) and those corresponding commands, if any, that use that keybinding will be filtered up.
Remember to disable the Recording Keys functionality by clicking the keyboardy icon if you want to go back to regular searching in the Keyboard Shortcuts file.