If it is a company, don't be scared to go the insurance route. Ring them with a quote you have had from a 3rd Party repair company. A few hundred should do the trick. If they don't want to settle out of insurance, then take it all the way.
Whiplash can take weeks to settle in after the initial shock. It sounds cheeky, but every bast*rd is doing it now, and if you had pranged someone, they would do it to you. After you become the victim of someone taking advantage like this, you will do it yourself, so get in first.
Whiplash is standard for a bang, and warrants a payout of around 1000-1500 without much question. Add that to the repair cost of the car and also any loss of earnings and the payout becomes astronomical.
You would be best advised to ring them up tomorrow (Saturday or Monday if they are closed w/ends) and ask them to settle the bill for the repairs. If you have any little scratches or what not on the car, you can get them fixed now too. Get a paint shop to get you a quote for that and ask them for a "Verbal" price on the rest of the little niggles.
You may find that they settle easily enough. If not, your looking at a fair few quid in your skyrocket come Next christmas or so. May be a nice Summer holiday 2008 for you.