My DD is going into yr8 at Parmiter's so can answer these for you.
No towel required, they barely get time to get changed never mind shower!
Football boots... Daughter never used them as football and hockey were on the astro turf pitches.
All clothing, blazers, bags etc, are locked in the changing rooms during the lessons.
The lockers for year 7 are next to the dining room and they can only be accessed at certain times, before school, break time, lunch time and after school not between lessons! These have to be booked from an outside company and cost £22/ year. My dd kept her PE kit in it and a spare pencil case. Worth getting so they don't have to carry PE kit round all day, some end up putting it down somewhere and forgetting it!!!
my DD suggests it would be better to wear crop tops...to save embarrassment
Hope this helps a little