Do below-the-line commenters have the right to remove their own comments?

A politician makes a joke which she later regrets. A footballer says something on the pitch which he quickly realises was unfortunate. A person leaves a comment beneath an article which he then wishes he hadn't made. All can now be found reported online accurately. All of these people have all expressed an opinion they later regret. Which of them have the legal right to have their words deleted upon request?
Current UK data protection law requires that for the use of personal data by an organisation to be lawful that it meets at least one of a number of criteria (legitimising conditions). They include consent, legal obligation, to fulfil a contract with an individual, to protect life, and so on. Consent is the most relevant here – consent can be given, and it can also be taken away. For example, you can agree to receive marketing emails, but you must be given the opportunity to unsubscribe from them too, as email marketing is consent driven by law. But does this give the commenter a right to have a comment deleted by withdrawing their consent? Probably not.
Journalism (as defined in the Data Protection Act) is exempt from the requirement to meet one of the "legitimising conditions", and for a number of reasons. Journalism is not a consent-based process under the Data Protection Act. Someone providing their opinion is not, strictly speaking, consenting to their personal data being published under this particular piece of law. It would be impossible for journalists (or those conducting acts of journalism) to ask for consent from the individual for every opinion they gather, for every speech they wish to report, and that's without even considering the requirements of investigative journalism.

Source: https://www.guardian.co.uk/commentisfree/2013/apr/04/commenters-right-to-remove-comments