I have admitted liability for an accident involving myself (a cyclist) and another car but dispute the amount the claimant has requested. I have hence decided to let the court decide on the amount I owe. My main issue is that the claimant has relied on an estimate of the costs incurred (carried out by an engineering consultant) and not the actual amount he had to pay for repairs. I am wondering if I need to make a court application (I don't really understand what one of these is) in order to make the Judge aware that I am happy to pay actual costs rather than estimated costs.
As a general rule, estimated costs are an acceptable means of proving damages in a car accident and it is not necessary to actually pay for repairs. Indeed, the car owner is free to decide to use the money awarded to, for example, buy a new car rather than repair the old one.
You could, in the proper manner make a filing with the court to advise it of your position, but the court is likely to disregard your stance since it is contrary to the other party's legal rights.
You would be better advised discussing settlement with the other party or their representative (usually lawyer or insurance adjuster or just individual), taking it out of the hands of the court where your prospects are poor.