Disconnect the supply at the first stop cock, and temporarily fit a
tap there. Run off vast quantities of water. If clear the problem is
on your piping, if not it's the water companies issue. If the problem
lies in your piping, bite the bullet, rip out all the old pipe and
re-plumb. Technically trivial though possibly physically challenging.
If it's your piping it sounds like you have iron barrel in use, in
which case it should be replaced anyway.


Andrew's proposal seems the most definitive test. But another (and less
invasive) experiment would be to use the stopcock in the road (which
you mentioned you had accessed before) to reduce the maximum flow rate
with the 2 taps to what you get usually with just the kitchen tap. Then,
if you still get the debris with the 2 taps running, it looks less
likely to be the result of the flow rate from outside your property and
more something within it. But it can't of course prove the converse.

Also, I think we've all assumed that you get debris in the water from
both the kitchen tap and the outside tap when running both. If
not.....


--
R