Insurance is a business based on gambling.
The insurance gambles that you will not cost them more than say, a tenth of the premium.
When you have a claim against them, they gamble again and offer you the minimum they think they can get away with paying you.
If you tell them your claim is worth £1,000 more, then they will gamble on whether they can get away without paying you.
They will look at whether you can prove your claim is worth the extra.
They will then look at whether they think you will settle for less, if say they offer you half of the difference...
At the limit - if you take them to court, they will look at whether the court will find in their favour, whether they will have to pay all the costs, whether it could damage their image.
Then they will decide whether to gamble or settle.
If you can convince them that they should pay you asap, rest assured, they will.
One of my cars caught fire one night. I managed to persuade the Prudential to send an assessor out the following day and agree to give me a third more than book price. I then convinced him to telephone the office and tell them to fax me the offer. I had the cheque in my hand 23 hours after I first called them.
Another of my cars was hit by a tractor. It had a 3 month old engine in it, and the plough weights broke the front of the block. They apid me the extra £900 the enging had cost on top of the book price.
You can do this. It takes determination, a little savvy and balls.