That's shit Graeme.
Car insurance has always been a big deal for me. I used to pay 465 a month with a 900 initial payment for my RX8, my postcode is the highest risk there is.
I admire their honesty, they're at work, it's work's insurance and so I doubt they'd help you out privately as they already pay their insurance.
I've had a bump or two and on both occasions, trying to avoid my premium climbing again (it's the lowest it's ever been now), I've offered to pay for all damage myself and did. I just said no to the "have you had an accident regardless of fault in the last 5 years" question as there was absolutely no record of it. His old Rover 75 he was very fond of would have obviously been written off, and my car had nothing more than a scuff, so all works out well. In the other occasion, she was a new driver, (she kind of caused it by being unpredictable, but I know that's still my fault, hence no debate), so she wanted to avoid her insurance climbing too.
Personally, I'd call them, see what they want to do, and if they're not offering to bung you the cash to have it sorted at your nearest bodyshop, claim on their insurance to have it fixed and never mention it again.
But that's just me and I'm a Mancuninan scumbag YMMV.