Hi Villiers,
Whilst not actually pertaining to your Tom Senior mill, I junked the inbuilt suds pumps on my machines and bought a central heating circulating pump, using the inbuilt tank on the Colchester, I welded in a valved outlet, rigid plastic hose connected the pump.
The outlet rubber pipe of the pump to the suds tap on the lathe was slit, just above the open top of the tank to act as a relief.
A tee piece was added to the base of the tap upright on the saddle, to feed the miller, with a return drain to the lathe tray, everything is kept together.
Everybody has their own way of accomplishing their own goals, so another approach may help you overcome your problem.
If you would like a photo of the setup, just say.