Hey John, thanks for taking the time to reply. The system is a current old Baxi combi boiler which is quite old (Probably 8 years plus, when I researched it's model number it's very famous for longevity and apparently landlords love them) Based on the pictures if you were in my situation do you think you'd replace or keep the copper?
I can only suggest what I would do - time and access permitting of course! In my own system (softish water supply - i.e no scale in the kettle)
There may well be a thin layer of magnetite in the pipes - this is iron oxide (two molecule) = rust but black rather than red.
I'd only replace the copper if it was damaged - kinked, beaten flat or whatever.
If you can flush the pipes out with mains water then great....preferably to each radiator valve if possible and one at a time. The flow and return pipes at the boiler will be bigger of course but are cleaned the same way.
The radiators - if you wish to keep them - will always have some black sludge inside which will ruin any carpet
so drag them into the garden and flush every which way with a hose.
If you wish to pressure test, only use water - never air. If any leak should occur the pressure immediately vanishes with water so it's much safer.
As I mentioned earlier, the feed pipe from the small loft tank must be flushed - this is where trouble usually starts as the rust and deposit is there unmoving for ages.
If you still have galvanised steel tanks in the loft, then replace them with plastic ones with a lid. Bale the small tank out with a wet vac to prevent any crap from going down into the system.
Good luck with your project - a quality inhibitor like Fernox is crucial, and a magnetic filter on the boiler return pipe is a very good move. Others will recommend one.
John