Water – Could work done to lower a radiator have caused a loss of water pressure from a combi boiler

My guess is there is a restriction in the line going to the house, with only enough getting through to feed one thing, either the toilet or the faucet. And since the toilet is probably drawing the water first before the faucet, it goes there.

I agree that it is more likely just heavy rain that is causing mud in your water. However, surface water getting into your water supply is bad news. You should consider adding filters to clean up the water supplied to the house. I'd guess a chlorine injector to kill any bacteria in the water, a tank to give the chlorine some time to do its job and let mud settle out, coupled with a filter that can take the remaining mud and chlorine out.

It appears to me you are building pressure using the bladder tanks. Once the pressure reserved in those tanks is depleted your pressure drops because the flow is restricted (possibly ahead of those tanks). I would agree with Justin that you have a restriction that is reducing the flow and after the bladder tanks are depleted you are only getting the flow through the main line.

The fact that it takes longer to fill the sink with pure cold water tells me your problem is a restriction in the line feeding the water heaters and the bladder tanks are compensating for this somewhat when you fill the sink with pure hot water.

Look for a restriction in your main cold water feed line, and then at other points in the system. Check the air pressure in your bladder tanks with the line drained. Lastly, the piping looks too small to me. I would upsize that piping for better flow.