Pump will not switch off?

I have an Autosleeper Talisman motor home, the water pump when switched on delivers water to all taps but also discharges water out of an overflow. The overflow is a clear pipe on the elbow that takes hot water from the Truma water heater. This elbow has no valve on it. I have replaced the one way valve on the system to no avail. The system is a pressurised one and once up to pressure the pump should switch off, unfortunately it does not. Is the solution a new pump or is there a cheaper alternative.
Thanks for any suggestions.
All the best

Chris