Whether or not the 3rd party insurer admits liability , ( even if court proceedings are issued ) will depend on who they view the negligent party to be .
Different insurers/defendants will not all agree , one way or the other , given the same set of accident circumstances .
I agree , without knowing what your and the other party's full account of the accident circumstaces is or seeing the locus ( accident location ) , or knowing whether or not there are any independent witnesses ; it is very difficult to give an opinion as to who is liable .
The other side may be arguing contributory negligence , going on the very brief allegation you have stated in your question .
However , how quickly liability is sorted out will depend in part on how pro-active your solicitor is .
If he/she is confident that the other party is wholly to blame , then he/she could make what is known as a part 36 offer to deal with the claim on a 100 % liability basis , in your favour .
Indeed , if medical eveidence has been finalised and agreed upon , your solicitor could also make a part 36 offer for damages ; at the same time
The response from the other insurer should give you a fairly accurate sense as to how they ( the other insurer intends to proceed )
Your solicitor Is obliged to inform you of the contents of any offer made by the other side , advise you on the offer , and take your instructions on the offer .