It is not the right place to talk about oil, but if I were in England I would also use the 10w40... for a climate reason.
I use it only in summer with minimum temperatures of 20 °C and maximum of 38 °C... I hold on to my 20w50 oil.
I close my speech on oil here, sorry out off topic.
Sorry for the red herring.
I wanted to rehearse what I thought is going on. The mini pump is not a straight forward gear pump so I have no idea how its output varies with rpm? But like all engine oil pumps output increases as speed rises. The only measure we have of flow is by pressure readings.
Resistance is dictated by engine bearing clearances as resistance to flow increases pressure will rise, conversely as resistance falls e.g knock big ends out flow increases and pressure drops. Thinner oils or hotter oils pass through the clearances so pressure drops as flow increases. Flow is controlled as Mark has correctly described it by a hydraulic shuttle valve which is pressure activated. We can adjust this pressure by the spring (or by using thinner oil) but bearing in mind this is a closed centre hydraulic system.
But I have no idea at what pressure the valve comes off the seat and opens. In a normal hydraulic system dumping pressure through a relief valve is frowned upon as it generates heat here we have no option. Oil coolers if effective will maintain oil pressure as the oils will be cooler as more viscous. Just to make life hard the pump picks oil up from a potentially dirty source the gearbox and it sends it to the shuttle valve before it is filtered. Hence some people prefer ball bearings as less likely to stick as they open (no experience myself). But both valves can suffer with debris on the relief/shuttle valve seat allowing oil to flow back into the sump. To be in command would you not need to run an oil temperature gauge as well as pressure? Or keep a close eye in this case on engine temperature?
Thats my thoughts for what its worth