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Tap the Settings app icon, which resembles a grey box with gears on it. You'll find this option about a third of the way down the page. It's near the bottom of the Safari page. Doing so will delete any cookies in your iPhone's Safari browser. Unfortunately, you can't delete only cookies in Safari on an iPhone. If you want to prevent all cookies going forward, scroll up to the "PRIVACY & SECURITY" section on the Safari page, tap the white "Block All Cookies" switch {"smallUrl":"https:\/\/www.wikihow.com\/images\/2\/25\/Iphoneswitchofficon.png","bigUrl":"\/images\/thumb\/2\/25\/Iphoneswitchofficon.png\/47px-Iphoneswitchofficon.png","smallWidth":460,"smallHeight":294,"bigWidth":"47","bigHeight":"30","licensing":"<div class=\"mw-parser-output\"><p>I edited this screenshot of an iPhone icon\n<\/p><p>License: <a rel=\"nofollow\" class=\"external text\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a><br>\n<\/p><\/div>"}, and tap Block All when prompted. This switch will turn green {"smallUrl":"https:\/\/www.wikihow.com\/images\/1\/15\/Iphoneswitchonicon1.png","bigUrl":"\/images\/thumb\/1\/15\/Iphoneswitchonicon1.png\/46px-Iphoneswitchonicon1.png","smallWidth":460,"smallHeight":300,"bigWidth":"46","bigHeight":"30","licensing":"<div class=\"mw-parser-output\"><p>I edited this screenshot of an iPhone\n<\/p><p>License: <a rel=\"nofollow\" class=\"external text\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a><br>\n<\/p><\/div>"}, signifying that your iPhone's Safari browser will no longer allow cookies. Keep in mind that some websites require cookies in order to load some features. Blocking all cookies will prevent some websites from working correctly.
Open your iPhone's  Settings. Scroll down and tap Safari. Scroll down and tap Clear History and Website Data. Tap Clear History and Data when prompted. Block cookies in the future.