Sludge in radiators.Are British Gas to blame?
BGS won’t have caused the sludge. It was almost certainly there before they added the inhibitor. Adding inhibitor after losing some water in the system is good practise and can do no harm. So I think you are on the wrong track trying to blame them for a condition that was there years before they came on the scene. Having said that. I would be disinclined to use them for the flush out. £600 is over the top. There are lots of firms that will do it for less. If it were summertime I would suggest that you did it yourself. You would need to drain down, remove each rad that was cold at the bottom (ones with sludge in) and hose them out in the garden, or down a drain. Reconnect and use a proprietary flushing chemical in accordance with the instructions (Fernox). Refill with inhibitor, job done. To do it thoroughly would take a couple of days, but its not rocket science as they say.