Safari favourites icons keeps changing places

You can disable sync of Safari here:

Settings → Apple ID → iCloud → disable Safari in the list.

You will be asked what you want to do with your previously synced data, select Keep on My iPhone to keep your favorites on your iPhone.

If you have other devices connected to your Apple ID, for example an iPad or Mac, your Favorites will also sync to them. If you have moved around your favorites on another device, you will see the same order on your iPhone - and may find that your icons move randomly.

You're welcome.