Well in fact the opposite. On close inspection of the pump there was a
distinct lack of noise, and the casing was blisteringly hot. It was
pretty clear that it wasn't functioning correctly.

My pump seems to be working, as much as I can hear it turning, but the
hot water does not seem to leave the boiler causing it to heat up until
it reaches the maximum tempratue causing it to trip out.

Could it be air stuck in the pipes preventing the pump from
distributing the heated water from the boiler?