thank you. The level of cover will be shown on your policy schedule but as above, unless you have specifically paid an additional sum for legal service, it would be unusual for legal cover to be included in standard though I have no doubt that the odd policy may include this standard.
if you do not have legal, which based on what you say seems more likely than not, the insurer would not have an obligation to defend your liability in a situation such as this. If you are unhappy in respect to the way they have dealt with the claim, then you can make a complaint but one of the most common complaints in this scenario would be where the insurer has admitted liability on your behalf which can restrict your ability to bring a claim as against the other party.
In the circumstances, because the insurer has settled without admitting liability, it is open to you to bring a claim against the other party for loss and damage to your vehicle and if applicable, any personal injury claim.
Accordingly, if you consider that you can demonstrate that the accident was either the other persons fault or at least one of contributory negligence, you could contemplate bringing a claim against them in the County Court in this respect. If the claim excludes any element of personal injury claim, then such a claim to be brought using the courts online issuing service:
https://www.gov.uk/make-court-claim-for-money