IMO the leak has to be addressed as leaking water can bring serious consequential problems if not cured quite promptly. [Like you I would prefer to fix things than trundle 150 miles, probably twice to take it back and later collect it, however its important you get the leak fixed even if as I suspect it does not relate to your pump running on issue]
The pump is likely controlled by one of two techniques that switch power to it on and off.
1) Each tap featuring an electrical micro switch that closes when the tap is opened. Each of these microswitches then powers the pump till the tap is closed. All taps then are fed with pressurised water, and water flows out the opened tap(s) till they are closed. The last tap closing severing the electrical power so the pump stops.
2) The pump is switched on if water pressure drops, and off if it reaches certain presets; this by one or two pressure switches. In this system with the water always at some pressure, any tap opening results in water flowing out of it and the pressure dropping switches the pump on.
These pressure switch systems (2) can be temperamental, they typically use a budget pressure switch that's sensitivity varies, and sometimes fails to act either switching on or off.
Any leakage of the pressurised water causes it to cycle, be that internal leakage back through the pump or out of the system. It would have IMO to be a very significant "leak" to keep the pump running continuously. I don't think your leak is cause enough other that the pump intermittently starting and stopping without a tap being used.
On this basis can you identify if you have a type 1 or 2 system?
If 2 can you find a gubbins in the pipework with a "knob" of sorts on it?