You are not squaring 0.1, You are squaring 10. It is 100 as you say and as such the calculation reading (£0.1)2 = £0.01 is far, far too simplistic.
Playing with the units simply doesn't work. You must keep the units consistent otherwise it all falls down, it is an extremely common trap to fall into in the engineering theory I used to work with.
Compare Apples with Apples.
Always conclude the calculations are doing before switching units.