Bit of a funny subject this, up until 6 months ago I spent 6yrs working as an insurance engineer in the motorcycle sector and met a lot of Assessors from insurance companies who would come to authorise repairs/write off damaged bikes. Now nothing on the road gets modified more than bikes, and you would be AMAZED how lenient they are.
Obviously it is at your own risk to not notify your insurers about anything, but you will generally find that if you have any mods that look 'OEM' it won't be too much hassle to get them repaired/replaced. We only found that the ins' co kicked up a fuss when the client was basically an a55hole - ie abusive on the phone to everbody etc, that the Assessors have the power to say "right, your exhaust is non standard and you have not declared it, therefore we are rejecting your claim an voiding your insurance" - 99.9% o the time, even race exhausts (illegal on UK roads) would get replaced. As a repairer we would go to the ends of the earth sometimes to obtain aftermarket equipment on bikes which had been damaged, an there was never any talk of whether it had been declared.
In addition to this, the same goes for things such as tyres being worn to/past the limit etc, depending on the accident - eg if a fatality has occurred then an engineer would have to determine if the fact that the tyres where bald would be an attributing factor to the accident then you would most likely get busted, however if its a simple bump between 2 cars, they won't be bothered, as it's too much paperwork, the repairer will just make you buy new tyres from them.
Personally, I pick and choose between mods, wheels for example I would, because they can be faulty and cause serious accidents, but things like black grilles etc I wouldn't bother because the Assessors wouldn't even know if it was not OEM and neither would they care to be brutally honest.
Bottom line is, as long as your car is economically viable to be repaired, and the modifications don't cause it to be Total Lossed unnecessarily then there most likely won't be a problem, as long as you dont cause a scene like something out of Die Hard 4 and cause a harrier jet to crash on the M5. The Assessors just work with numbers, ie is it repairable? Yes repair it, is it repairable? No write it off. Simples.