If I was at fault but the extent of the damage was not worth claiming on my insurance,am I entitled to ask for more than one estimate?

Yes

Or instead, has the victim got a right to have the vehicle repaired at a garage of their choosing?

Yes, subject to a reasonable price.

The person concerned has a duty to mitigate costs. Thus the repair must be completed to an acceptable standard at the lowest price reasonably available. Usually when this comes up someone is demanding a "main dealer" repairs their car. Firstly it is extremely unlikely that the "main dealer" will repair the bodywork - they will send it out - and secondly they will load the price so it will be more expensive.

If the person fails to "mitigate costs" then you have a potential claim against the non-fault driver for the difference between which a repair could have been undertaken to an acceptable standard and the cost actually charged.