The pressure was good. I removed the non return valves from the shower earlier on advice from Crosswater so the hot would not be closed but could be overpowered as you describe. There are no flexible pipes, valves or connectors in between the shower pump and the showers, though the extension on to the bath was recently added when the new shower was installed. This was via a Tee-off on the pipes going up the wall to the shower, this is however all in copper pipe to the bath diverter valve.
Not sure what else it can be as it doesn't seem to be the showers, the pump seems ok, but definitely something wrong with the balance between hot and cold, though would expect the pump to normalise that. One point that I would have liked to check was the valve on the hot from the cylinder to the pump inlet, I cannot tell how open or shut this is because it is seized up as are all the gate stop valves. If this was restricted I guess that would inhibit the amount of hot able to pass to the pump. I have no evidence that there is a problem and the expectation is it would be fully open.
Not sure what else it can be as it doesn't seem to be the showers, the pump seems ok, but definitely something wrong with the balance between hot and cold, though would expect the pump to normalise that. One point that I would have liked to check was the valve on the hot from the cylinder to the pump inlet, I cannot tell how open or shut this is because it is seized up as are all the gate stop valves. If this was restricted I guess that would inhibit the amount of hot able to pass to the pump. I have no evidence that there is a problem and the expectation is it would be fully open.