It's been said: magnetite, but in the rads, not the pipes. Your system, from the picture, looks like it was a disaster waiting to happen: 1970s or 1980s system, possibly without any sort of cleaner fitted and possibly without corrosion proofer.
I had one like that!
So here's a guess as to what happened: over the years, your radiators have corroded and collected sludge, which collects in the middle of the bottom tube, where the water flows the slowest. Normally it doesn't get in the way, although it will settle in slow pipes and clog slightly open valves. Draining to change the boiler disturbed all this, and the sludge is now blocking things, and putting your new boiler and pump at risk, too.
You need a power flush, including all the rads AND the boiler - everything you can get at, in fact. You need a Magnaclean fitted, to collect the sludge that isn't flushed out and keep your boiler safe, and for the next six months you need to clean it religiously, ideally every fortnight. You need a proper dose of good corrosion proofer when its finally refilled - Fernox is still very good, but in my limited experience budget brands aren't.
I suspect the plumber knew all this, but power flushing is labour-intensive (I had to postpone our maintenance flush this year - two days of our plumber's time was too much for us!). It should have been part of the quote: as others have said, putting a new boiler onto an old system is asking for trouble unless you do it.
I skim-read a lot of this thread, but if there was a flood changing the pump, that's often a sign of a lot of crud - in the 1970s through to the 1990s, pumps typically had gate valves (a sliding barrier, like those on lock gates), done so that when open they don't interrupt the flow. They're easily jammed or stopped from closing by crud filling up the bottom of the channel the gate moves in - they'll feel closed but they aren't. Aside: modern fittings are often ball valves (a rotating sphere with a hole through the middle where the water flows). They're more compact and don't jam as easily, but only on-off (gate valves can regulate flow, too).
If the above is correct (did the water come out black initially?), you may have other problems not yet apparent: There is a mode of corrosion known as de-zincification of brass. Brass is an amalgam of copper and zinc, and chemical action preferentially removes the zinc from the metal matrix. Result: It goes cheese-like, loses a lot of its structural strength, and can even weep as pinholes are created. I once actually saw a kitchen tap drop off the end of the pipe coming out of the wall - all by itself with no warning!* This happens to radiator valves particularly in systems that haven't had corrosion proofer for long periods. You usually find out when you try to undo a fitting and it crumbles or squashes as you spanner it. The only cure is to replace the fittings affected.
Steps to resolve it properly: ASSUMING THE SYSTEM WAS FITTED COMPETENTLY IN THE FIRST PLACE, flush the whole lot well, paying particular attention to the new boiler, pump and associated valves, including the 3-way one that does the hot water. While it's empty, check that all the rad valves move properly, especially those on the lower floor circuit, not too loose, and no grinding when you turn them. Change any you're doubtful about. Fit a Magnaclean to protect the boiler. Re-fill with a lot of corrosion proofer (more than manufacturer's specification). For the first few days running, go round everywhere checking carefully for leaks. Look around the time the heating comes on - water is flowing but the system isn't so hot that a small leak will evaporate. I use loo roll - hold it round the joints and see if it gets damp.
I'm not commenting on your plumber(s)! I've no idea what was said at the outset, or if you had an absurdly cheap quote or whatever. A lot of the work in changing a boiler is all the other stuff - flushing out and fixing up the rest of the system. That's why it usually seems like an expensive task.
One final thing: there should be a 'bypass' in any system with thermostatic valves. It's a path for the water to circulate if all the thermostats are off at any time. Traditionally this was the bathroom towel rail/radiator (always on), but sometimes it's the last radiator on a run or just a pipe joining the flow and return. It's worth checking with the plumber where/what this is: when it's all working you need to balnce the flow all round, and this bypass needs to be set to the minimum sensible flow, so it doesn't 'short circuit' the heating water. Otherwise, your rads won't get warm and you'll be scratching your head as to why. Once set it can be permanently left alone, but it's helpful to know if it *is* a bathroom rad, in case someone fiddles with it.
You might also want to make a note of how much each rad valve is turned on or off. It only matters for the lockshield valves (other end from the thermostats), as they stay set. You'll then know how to reset things if, say, you remove a rad for decorating later on.
E. (amateur plumber, albeit with 35 years experience)
*It was in a kitchen in Kathmandu - I was sitting at the opposite side of the table having breakfast. The tap fell into the sink. The open pipe shot water across the room, like something from a Buster Keaton movie. Why? Steel pipe buried in a high-lime-cement damp wall, and the back of the tap had been plastered in, in effect making an electrical battery and circuit, making the process much more agressive than normal.. By the time I got home from work that evening, they'd dug into the wall, replaced a section of steel pipe and fitted a new tap. They left a longer length sticking out of the wall, so it couldn't happen again.
