A - In answering this question I am going to ignore the issue of whether permission to do the cover version in the first place has been obtained or is necessary. I am also going to ignore the possibility that there may be a contract in existence between the original songwriter and the person doing the cover. Obviously, if there is a contract in place then the answer to the question would likely be determined by the terms of the contract.
Under the Copyright and Related Rights Act 2000, artists have the right not to have their work subjected to “derogatory treatment”. This is one of several “moral rights” belonging to artists.
“Treatment” of a work means any addition to, deletion from or alteration to or adaptation of the work. Treatment may be seen as derogatory if it amounts to distortion or mutilation of the work or is otherwise prejudicial to the reputation of the author. It is not so easy to prove that someone’s interpretation of your music amounts to a distortion or mutilation. While you may not like it, others may think its better than your original version. The essential point is that just because you believe a cover version is crap does not mean the original work has been mutilated (though at a practical level you may feel differently!).
An artist may also invoke the “derogatory treatment” right by proving that the offending version is prejudicial to his or her reputation. To start with, therefore, you would need to have a public reputation to protect. If you have little or no reputation in the market place then you may not be able to invoke this right. If you do have an established reputation, then you would have to prove that the cover version itself is harmful to that reputation. Generally speaking, bad cover versions tend not to harm the reputation of the original artist – they are more likely to harm the reputation of the person doing the cover (leaving aside parodies/ironic versions which are often well regarded). An obvious exception to this would be the use of a cover version as a soundtrack on a porno movie.
In any event, when considering an offensive cover version, it can be difficult to prove that either (i) your original song has been mutilated; or (ii) your reputation has been harmed by the cover version.