In the UK there are no specific celebrity protection laws
but it is illegal to place the image of any living person within a derogatory context or use their image for a commercial purpose (without their express permission). Using a person's image for commercial purposes could expose you to a potential legal action for defamation and for ‘passing off'. ‘Passing off' means that an infringement of the law would take place if it could be inferred from your artwork that a link existed between you and another person when this was not the case.
You should also be aware of the risks of basing your work on any photographs of a celebrity, as you might also be infringing the photographer's or publisher's copyright.
If you plan to use the image of a celebrity in your work, take particular care if you intend to exhibit in the US. Personality / celebrity rights are protected by both federal law and in around thirty states. The strongest and longest of such celebrity / personality rights legislations is in California, which gives the right to prevent the likeness, signature and voice of a celebrity from being used commercially and lasts for the lifetime of the celebrity plus seventy years after their death. There is an exception under this law that allows the likeness etc. to be used in unique (but not multiple) works of visual art.