I think you have summer strawberries rather than perpetual, and they are unlikely to have enough fine weather to develop and ripen fruit now so I would not bother with fleece. It is true that fleece keeps some light off and this makes more difference in sombre autumn days than bright spring ones. I just noticed today how some fleeced Red Frills mustard is paler than the unfleeced.
If we have the promised lovely September, your fruit may ripen in October but I have found the flavour is less exciting then, from a lack of sun and sweetness.