Apple watch still paired to an iPhone I no longer have
One thing you can do, assuming you're not worried about losing the data on your Apple Watch, is to erase all content and settings on the watch itself. However, if you have no access to a backup, then you'll be setting the watch up from scratch as a new watch.

If you want to proceed, the process is as follows:


Launch the Settings app on your Apple Watch
Tap on General
Swipe up and tap on the Reset button
Tap on Erase All Content and Settings
Tap on Erase All


Once complete, your watch will be back to factory settings. You can now go through the process of pairing it with your new iPhone.

NOTES:


In your situation this is unlikely, but if you're prompted to restore from a watch backup, then select the latest backup you have. 
Since you're not likely to have an iPhone backup, you’ll just have to set up your Apple Watch as new.


[UPDATE]

Since you've clarified in the comments that you can't actually even touch your Apple Watch screen without getting prompted about a wrong code, try these steps instead:


Put the Apple Watch on its charger with the power on (so that it's charging) and keep it on charge for all of the following steps!
Press and hold the side button (not the Crown) until you see the Power Off slider
Press hard on the Power Off slider for about a second and then remove your finger
Tap on Erase All Content and Settings
Tap on Erase All


Once complete, your watch will be back to factory settings. You can now go through the process of pairing it with your new iPhone.