Sentinel and Fernox are good brands of CH chemicals and are widely available.
I've heard you need to leave the Sentinel cleaner in for a few weeks to clean away all the stuff.
There is a Fernox one called DS40 which is very strong, maybe hold off on that for now if you think the system is in poor condition. I am just householder, not a heating engineer but have done these things in my own house. Although people sometimes say the cleaners have caused leaks, what they really do is to remove scale and sediment that is blocking existing holes.
Is your blockage hard black sediment? If so, there is a device you can buy that will capture any of it that is circulating loose in the water with a magnet. This prevents future build-up. If you fit one on the pipes leading to the boiler, it will trap loose sediment that might otherwise collect there. The Magnaclean is a good one, and will cost you in the region of £100.
If you can flush away much loose stuff, it will allow your cleaning chemicals to get to work afterwards on the remaining hard residue.
If you have a blockage of scale from hard water, you probably have a leak. Otherwise, the same water just recirculates, and does not add further limescale.
If you have had sediment circulating for a long time, the pump may well be worn, but it is a replacable part if it fails.
Have a go at taking out the F&E and renewing the pipe, it will probably save time in the long run.
It sounds like you will be doing a lot of flushing and draining, so consider fitting a full-bore drain off tap. It will make draining a positive joy in future
and will flush out more grime.