Just to be clear here, the £600 excess is the contribution you would pay if you make the claim on your own insurance for your own damage. Regarding third party damage (the car you hit), insurance companies are obliged to pay out third parties in full. That's what insurance is there for. It's highly likely that the third party's representatives will be contacting your insurance company for all sorts of claims (damage, whiplash etc.) so it's in your interest now to tell your insurance company about the incident if you haven't done so already. You don't have to claim for your own damage if you'd rather sort that privately. Your policy terms and conditions will include a requirement to notify your insurers of all relevant incidents without delay.
You won't have to pay out anything short term, unless you're claiming for repair on your own car. Of course, the collision will now be noted on your record and you'll lose your no claim discount. Your premium at renewal will probably increase, and you'll have to declare this incident at every renewal and quotation for the next few years, whether you claim or not.