Time to eat some humble pie and admit that I was totally wrong in my selection of footwear. However, the experiment helped me realise that nothing beats investing in cycling shoes so time for me to pull my money out.
With the shoes featured in my previous post the thin sole put me in too much contact with the pedal requiring more force in every stroke. I was teaching on a Keiser bike and realised that I could not hit 400 watts plus so easily.
The flimsy nature of the footwear meant too much flexion at the toes and I felt the traction at the back of my knee and slightly in my lower back. Hence, a rigid shoe is better.
A thin shoe will not fit into the pedal cage adequately so the foot is not stable. Hence, regular sneakers/asics that you use for running are probably better as it is more likely to fit into the cage well.
In any case, normal footwear will not allow you to maximise the use of the ball of your foot as with the pedal clips you have to apply pressure in the middle of the foot. With cycling shoes you can apply pressure more at the ball of your foot and this may improve performance greatly.
At least I am happy with the way my new trainers look but after I return from Italy I will look to invest in some cycling shoes and see the difference they make.
Many thanks to Tom Joka and Andrew Frimpong for assisting me with their knowledge on this subject.