Hello, I am a lawyer with over 15 years experience. I will try to help you with this.
It does seem that this may be an attempt to make some money at your expense. in order for me to answer fully can you tell me the following What is the name of the claims management company? Does their letter to you justify how they have come to the figure? Did you take any photographs of their car or yours? Is their car a particularly expensive car?
We have had no correspondence from the claim company only a telephone call when they gave their name as ACH - we understand this to be Accident Claims Helpline, We have asked them to email a copy of the repair bill but this has not arrived, We did not take photo of their car but can photo ours. The make of car was a small peugeot - not expensive
Probably the thing to do is to wait and see what happens. If they send you a letter setting out a claim and demanding compensation you should reply to it stating what happened and that you do not accept their valuation. That your car had similar damage and was repaired for less than £200. You will obviously state there was no need for a courtesy car due to the minor nature of the damage. You could offer something reasonable. If you have the other driver's details you could do it directly with them or with the claims company. You do not have to deal with the claims company.
It would be a good idea to offer to pay what you think is a reasonable amount. Even if they have incurred a very expensive repair bill you do not have to pay this if they could have got it done equally well at a more reasonable price.
Ultimately they will have to go to the small claims court to claim any money you are not offering and prove on the balance of probabilities that they incurred those costs and that they were reasonable. It is likely that this is an attempt to scare money out of you and if you resist they may well give up and move on to see if they can find an easier target. If they bring an action you can defend it without the need for solicitors. .
This answer assumes you accept it was your husband's fault I assume this because he offered to pay).
Now that the level of alleged claim has reached the level it had you may want to think about involving your insurance company but you will need to balance the value of their help against the effect on future premiums.
I hope this is a helpful answer but please feel free to ask further questions.
My husband did not think to obtain the other drivers details (he now knows better!) Can we require the claims company to provide her address details or ask that she contact us. At the moment we do not know who the claims company is working for - her or the repair company.