Pressure too low to activate pump

[Handy Hero]

Dear All

A good customer of mine got in touch about her toilet taking half an hour to fill because the pressure is so low. There is a pump on the system but it doesn't activate because the flow is so low.

Can anyone suggest a pump that will activate at the slightest flow? Mains feed is possible but not easy.

I'd appreciate any suggestions but especially from first hand experience - I don't want to fit a new pump unless I'm very confident that it will do the job.

Thanks very much.