insurance claim
As part of your contract with the insurance company, they get the right to handle claim against you. Technically, the insurance company appointed solicitor is representing you in court, so the question of you being separately represented in the court case does not really arise.
There was a common problem in times past that insurance companies were too ready to settle claims for "nuisance value" rather than go to court. This sometimes left policyholders such as yourself feeling put out that a claimant had got money to which they were not entitled, and that a no claims bonus had been sacrificed to expediency. This is much less common today, though the court process undoubtedly still leaves some policyholders feeling disenfranchised.
There is an argument to be made that the insurer - either explicitly or implicitly - has a contractual duty to you not to pay out in circumstances where it shouldn't. It is also argueable that a letter from your own solicitor to the insurer might keep the insurer's mind focused on this, so there is some merit in you consulting a separate solicitor, but for the reason stated above, you will not be separately represented in the court case itself.
If you are a big customer, it is possible to negotiate with some insurers that you will have choice of solicitor for defence of claims, but if you were that size of customer, I expect you would already be aware of this.