The distance from the water level in the tank to the top of the tallest
radiator is approx 1 metre.

That should be plenty of 'head'. My header tank is slightly less
that one metre above my two highest radiators. They are always the
ones that accumulate the most air.

If you want to experiment, try attaching a piece of clear poly
pipe to your highest radiator and see how high you have to raise the
open end in order to stop the water from over-flowing. This will then
indicate the water height in your header tank. Oh, turn the pump off
first and don't scald yourself.

Chris.