I don't think asking for an emg will make them think you're crazy. Over the years I have learned you have to be really persistent when you know something is wrong but doctors don't figure out a diagnosis right away.

I'm not from the UK so I don't know what would be the best way to approach this. If you can't get an appointment to see another neurologist soon maybe you should go to the ER? Either way don't give up, insist that they continue to do tests until they find out whats wrong.