Insurance company won't pay third party because I had modified my car with bigger wheels

You need to disclose any modifications you make to your car to the insurers. They are very strict about this and they even have a clause in their policy which invalidates your insurance if your car is not as you described.

There is reasoning behind this, let me explain.

Modifications can make you more prone to accidents

If you have a little Vauxhall Corsa, your premiums would be very low compared to other cars with bigger engines. Let's say you modify this and get turbo installed which allows you to drive really fast, now you're more likely to drive faster than normal (because you can!) and your risks of getting into an accident are much higher. You therefore have to pay a bigger sum to get insured and not expect to pay the same kind of money as if the car was in standard manufacturer condition.

Modifications cost the insurer more money in repairs

The insurer is supposed to give you a like for like in the event of an accident. If your car is now built for speed, damages you would do will be more expensive to restore, both to your and the 3rd party's car. Your modifications may mean the bits and bobs are not in the usual place, which means more labour and the parts themselves may be more expensive because they are not the standard fitted.

With all that said, you just need to be as honest as you can be about the description of your car, even if it deviates a tiny bit from the manufacturer's standard, because insurers will try anything they can to not pay out in the first place if they can.

Final Note

One thing worth mentioning is that you can fight your case in court because it's up to the insurer to prove the accident was caused by the modification you've made, otherwise your insurance remains valid.

Good luck.

When you are getting a quote, you have to say if it's modified or not as this effects your quote.