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Doggit
Just what sort of hot water tank have you got. If you were to turn off the cold mains, or tie up the ballcock on the cold water storage tank, so that water couldn't flow through, then the leak would slow down.
The Pressure in the CH will rise as the boiler starts, then then sink back as it cools, so no problem there.
The Pressure in the CH will rise as the boiler starts, then then sink back as it cools, so no problem there.