It depends on who the repairer is. I would only go to the insurer's repairer if it was a proper bodyshop with a good reputation locally.
I had a prang last year and was offered by my insurer a company called Nationwide Accident Repair in East Grinstead. Odd because East Grinstead is 25 miles away and there are a number of insurer-approved repairers locally. I had I suspicion that they were some crash repairer working for the motor trade and the reviews on google were mainly bad, so I went to body shop ran by a local dealer chain. They are not Honda approved but were for Toyota and Nissan which was close enough.
If you go to a Honda approved body shop make sure they are insurer approved and ask if they do the work themselves or do they use a bodyshop to do it on their behalf. If it's the latter it maybe cheaper to approach that bodyshop directly.
Although you say you have access to another vehicle, I will still point out for the benefit of anyone else reading this that your insurer may not provide you with a courtesy car unless you go with their designated repairer, if such is included on your policy. As the guy who hit my car drove off without stopping, I didn't want to foot the bill to insure my chosen repair's courtesy car on my policy, but when I pointed this out they stepped in and offered to pay for the cover on their car. So don't be afraid to ask - they may say yes if they want your business!
