is identity theft illegal?

[Jon]

It is not a crime to display a picture which is not of yourself on a website. It would similarly not be a crime to use a false name unless there was an intention to gain money or property by the deception. E.g. there is no law against someone who imagines their name sounds boring inventing one they think is more interesting.

If the person involved here is not only using another person's image but is also using their name and in general pretending to be that other person then while this is not itself illegal it could easily become so (and it will be against the terms of use for many websites). Impersonating another real person (rather than using a fictitious false identity) could become illegal if the imposter did anything which had a harmful effect upon the real person. An imposter who damages a person's reputation (e.g. by claiming to be that person and boasting online of criminal or immoral activities, such as having an affair, when the real person has not done such things) could be guilty of libel. Such online imposture may well also break the Malicious Communications Act.