You'll be surprised quite how much that costs to repair.
The 4k doesn't sound unlikely tbh.
The bumper alone will probably cost upwards of 1500 quid once its been sprayed...
I'd use your insurance - sure your premiums will go up for 5 years, but I doubt if the increase over that time will amount to what this is likely to cost to fix.
Protected no claims btw won't help you much - the discount to the premium will still be applied but the actual claim will still be factored into the premium.
Its a pain in the butt and I feel for you