As others have said you shouldn’t be charged the excess if the other party has accepted all responsibility.
Here’s a long story for you, on the 2 occasions I’ve needed to make a no fault claim there has been no charge but on my last claim when my current car was just 3 months old and rear ended RSA made a threat I would need the pay the £100 because I got one of the letters of the other party registration number wrong. There was no problems with anything else as other parties phone numbers and address where correct so a simple thing to fix but I had to ring the other party personally to get the correct reg.
I also made it clear to them that its not easy for a lone disabled driver to gather witnesses and walk around cars surveying damaged and they should know better.
I also told them as my car was safe to drive and roadworthy and they could not have the car back for repair until a suitable replacement was found including a hoist and parked outside my house.
They tried to get me to use taxi’s and again told them this was a no fault claim and that 3 months previously I had paid £1,800 AP for the car so refuse to use taxies. I might have sounded cantankerous to them but this was a no fault claim and maybe I would have been less cantankerous had I been partly to blame.
They found a hire car a week or so later that was exactly the same make, same model, same trim level, same colour with even the same hoist in the back and cost £400 delivery from London to Bristol and from memory about £250 per day hire and I had the car for 2 weeks.
I was a bit disappointed with the hire car being the same as mine because I was told it would be a Ford Galaxy and would have loved a long test drive in that but wasn’t to be. ?