You can make a subject access request to the police for a copy of the information they hold on you locally. It might well be redacted to hide names, but other than that it ought to include the report. There is information on the Unlock website about this here
. As Square
says, Google are unlikely to want to take down the links, and will probably claim it is in the public's interest, but there is a difference between the public interest and what interests the public. If your report from the police is favourable, it might support an argument that it is no longer in the public's interest, but you might well end up needing to take legal action. Unlock has information about this as well, which you can find here
. The law on data protection changed on 25th May, but I have no idea if the changes will help you.
As Chris Stacey said: Although its not formally part of the sentence that is handed down in court, the criminal record that someone comes away with effectively becomes a second sentence, which can have a long-lasting, if not lifelong, impact.