Is there a way to recover permanently deleted photos from an iPhone?

You wrote:

"...Although I had deleted them from my "Recently Deleted" album I still cannot find them in my Photos app or iCloud..."

I am afraid you misunderstood how the Recently Deleted album is working. Deleting from "Recently Deleted" does not recover the photos and revert the deletion, it does the opposite as Mark explained. You have to select the photos in Recently deleted and click "Recover".

The sad thing is, that you seem to have been using iCloud Photos, when you deleted the photos. Deleting from Recently Deleted is deleting the photos from iCloud Photos as well. And the photos in our iCloud Photos Library are not saved in our regular iCloud Backup of the iPhone either. Using iCloud Photos is disabling all easy backup methods. Have you made any backup of your iPhone on a computer? A backup on the computer may include the photos, that have not been optimized on the iPhone by iCloud.

If you have no backup of your iPhone on a computer, I recommend to contact Apple Support for help and explain, that you misunderstood how the Recently Deleted album is working and ask Apple to recover your iCloud Photos from their own backups. Only Apple can help to recover items from their own backups. Perhaps they will oblige to help in a desperate case.

Unless you have a back up, those images are gone - the key word is permanently. That's what it means. They are irrecoverable.

If you change your mind about deleting a photo, you have to recover it from Recently Deleted to get it back. As you have found, if you delete it from Recently Deleted, the deletion becomes permanent.