You can swipe left to delete items in your reading list one-by-one. I am still trying to come up with a way to delete them quicker as I have several to get rid of.
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To delete items from your Reading List on an iPhone, open the Safari app, tap the bookmark icon at the bottom, select the glasses icon to access your Reading List, swipe left on the item you want to delete, and tap "Delete" to remove it. You can also tap "Edit" in the Reading List screen to select multiple items to delete at once.