Dd1 is at an independent girls school and the library is open every day after school till 5pm.
We are looking at schools for dd2, she'll sit for her sisters school but also others. We are considering a girls grammar, one of the top ones in the country. But I was surprised to find out their library is not open after school, only at lunch time.
Yes, most days when something is going on. But until the school closes for the evening there are always corridors where kids can work as well as computers all over the place. We have hundreds of reference books at home for when its shut.
You will be amazed how many books you can downloand for free form the e-readers. Just type in free books. All the "classic novels". DD also reads as yet unpublished books looking for an audience (more variable quality but really has helped her understand what makes a good writer and a poor one!) So no we don't like to waste money either!
I teach in an Outstanding school. Our library is open after school from January until the end of the exam period. The librarians are only paid to work during school hours, so this relies on staff volunteers (interestingly, usually the same staff who do clubs - gluttons for punishment!). Some students are 'asked' to attend these sessions others volunteer. Our results are very good.