It is a big house so I think it was 22 in total when I had to count them all for the powerflush quote!! Several are very new but others could easily be 20 years old. I was chatting to our regular plumber on the phone whether we could remove one of the older ones and inspect it to see how full of rubbish it is.How many rads have you got? Probably only a few hundred to replace them all if you have basic plumbing skills. Imagine 10mm of crud in a radiator - the chemicals dissolve 5mm, you've still got plenty left! The pipes should be ok assuming you have good circulation round the system.
We might look at flushing them individually and replacing the older ones. If it's something that needs doing because they are at the end of their life, delaying isn't going to save anything - we set a pot of money aside buying an old house knowing we would have things like this. Replacing radiators is far less stressful than having to pull floorboards up to access the pipes though it sounds like they'd all need doing at once to avoid new ones getting 'contaminated'?