UPDATE
Thanks for all the advice and interesting ideas!
To answer a few questions - the water comes via a spring into the property then direct to the cold water taps (through a fibre cartridge filter first), there is a tank in the loft but only to feed the hot water cylinder.
The boiler is...
I'm not sure (it is shared with a couple of farm properties) - the flow depends on the weather (i.e. amount of recent rain) and is quite dirty when it arrives at the property before going through a cartridge filter.
I think I'll give this a go to get the water in then try the suggestion below...
We recently inherited an old house and the cold water supply comes from a private spring and is generally low in pressure (can easily stop the flow with a finger over the tap).
The property has a relatively new (< 5years old) condensing boiler.
The rads were full of air so we bled them but now...