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We have two like (but not identical to) this: https://www.diy.com/departments/pack-of-2-indoor-outdoor-small-humane-mice-mouse-rat-rodent-trap-catcher-cage/5021196016670_BQ.prd
I'm going to try gluing a penny or two to the trigger pad today, because we've suspiciously never caught a solo mouse. The two I caught together were tiny. Your house mouse sounds terrifying - like one of those angry young men on steroids who scream at you from a BMW 1 Series.
Sparky-
The trap I linked to was really good for me, mechanism seems different to the one you have. I would regularly catch mice with it and relocate them to the park near my work. The 'roid' mouse was a bit of a one-off but I still caught it eventually and just put the whole thing in a metal saucepan so it couldn't escape/chew its way out.
Tonts
If you want 'the business' then a longworth small mammal trap is the answer.
I did fine with something like this: https://www.espares.co.uk/product/es1642922?
However I think we were mainly getting field/wood mice ventureing into our house. Once we caught what I thought was a house mouse and it rattled the thing so hard it escaped. Then when I caught it again, it chewed it's way out of a recycling box.