The Association of British Insurers and the Financial Conduct Authority agree that getting a car repaired at any garage is your choice. But, there are certain exceptions to this rule.
Many insurers have their own network of approved repairers and insist you get your car checked at those centres for their convenience and not yours.
You are entitled to consider the benefits of dealing with the garage of your choice including the trade-in value of your vehicle (as manufacturers' warranties are maintained) and the consumer protection of a recognised code of practice. You may also have obligations under contract hire or lease agreements.
If your policy promises you a courtesy car whilst yours is being repaired, it may stipulate that this will only happen if you use the insurer's chosen repairer, which is not true.