no, it is not suggested to send anything to the visa office until it is requested. if you wish to get a back up just in case it's requested, there is nothing stopping you. the general rule is if cic received the report within 90 days of it being issued, then another one will not be necessary. there is no guarantee. right now, it's best to sit tight and wait it out.
if your application has been with london for 6 months, then you are still within the posted processing time, and there isn't much else to do other than wait. i would suggest finding the london applicant thread and adding yourself to the spreadsheet if you haven't already. this is where you'll be able to understand the "Trends" for applications at that office. I believe the current processing time for london is 8ish months.