Make sure you are running iOS version 13 or newer (If not, please update your device).
Go to Settings > Safari > Downloads > Choose "On my iPhone"
By choosing "On my iPhone", the videos are downloaded to your phone and you can easily share them via other apps, such as Instagram, etc.
Next, follow these steps:
- Open the video or album in the Safari browser.
- Tap the Downloads button on the top right, and it will open a Downloads box with a list of downloads (shown below).
- Tap and hold the "Download" button beside the file you want to open (outlined in red). This will open a menu (shown below)
Note: Simply tapping the download button will open the video in another tab. So, make sure you "tap and hold".
- Tap on "Download Linked File" and the video will start downloading.
- You will be able to see the progress of the download on the top right of the browser.
- Once the download finishes, you will be able to see it in your Photos app in the Downloads folder.