accident - my car hit from the rear, who's fault?

Hi all, wondering if I could have some advice. So here is my case in points...
*there was a very slow running /standing traffic on the road (picture made as a proof)
*my car was not moving (queue of the cars on the line ahead)
*my car was in correct slightly right front turned position with an indicator and lights turned on, prepared to change the line (waiting for space gap between cars slowly moving on the other line)
*my car was suddenly hit in the rear bumper by the third party driver from the back
*I pushed the brake to avoid crashing into some else on front of me
*the third party driver came out of his vehicle and apologised ‘’ sorry, I didn’t see you’’
* The third party driver said he has no insurance details with him and to forgive him as he is new driver and never been in this situation
*I said I am happy for police to come in this case
*The third party driver promised to provide his insurance details as soon he will get to place he was going to ( therefore for security I have taken images of his car and driving licence)
*The damage to third party car was none/barely noticeable – image taken (bumper halogen lamp maybe slighlty scratched)
*The third part driver still not provided his insurance details so I called my insurance company with details I had - his car registration plate and name, must add in a mean time the third party drived called me and said i need to do some research as i don't know what to do...then after I report it he said ''oh we could sort it between us''
Despite I thought it's not worth to make a claim but just report it - suddenly few weeks I have received letter from third party blaming me...I have responded and made accident drawing they asked for.. Another surprise!!! Received a letter they want to split blame 50/50, but I can't see my fault here... Please help