You have absolutley no chance of a broker back dating a cover note. Why would risk losing their licence and risk the fact that you may have already had an accident and just want to claim!
Also, when you go to the police station, there is no point taking any 'evidence'. You are either covered or you are not. If you are not, the police will simply report you for having no insurance. They cannot say "oh i see what you mean, never mind, we will let you off". Its not up to them. They HAVE to report you and its up to the court to decide. Thats where you can take your evidence.
I know you will probably take it to the police station anyway and try your luck but I just want to fore warn you.
I know this from experience (ie the other side of the desk)