The first book store is Junkudo, on the main shopping street. That this chain sells English books is not listed on their website or in the store. Even so you can find a few long rows of new novels in English on the 5th floor, near the pay desk. They might even have some other languages, I'll check that maybe next time. They have the biggest collection in Kyoto, what I have found. You can find the classics, the popular writers, many books-turned-into-a-movie and some special interest books even. For instance books for tourists 'where to find the most beautiful cherry blossom, the best gardens or other touristy things to do' in Kyoto, or Japan.
BAL building Floor 5 ~ 8F
〒 604-8032 Kawaramachi
Yamazakicho, Nakagyo WardKyoto
Another store selling books in English is called BookOff. This chain actually has ten stores in Kyoto. They sells games, DVD's and are known for their second hand sections. I tried two off their branches in Kyoto for an English section. One is at the top floor of OPA, a department store for teens. You can find OPA also in the shopping center. It has a smaller section of English books than Yunkudo, and they are all second hand, from 100 yen. On the same floor you can also find art books in English and special interest books. The other BookOff branch I checked with success for books in English is the one at Keihan Sanjo station. This branch also has novels and art books, although on different floors. I rather test my luck at one of the BookOff stores, because you can't really go wrong with these prices.
Bookoff at OPA Floor 8F
〒604-8026 Kawaramachi Shijo
Kawaramachi, Nakagyo Ward
BookOff at Station Building Keihan Sanjo
〒 605-0009 Ohashi
Ohashi Sanjodori, Higashiyama Ward
The last one is really more of a shop you would turn to in case of an 'emergency'. The bookstore can be found in the building of Kyoto Station, between the Shinkansen Central Entrance and the Miyakomichi fountain. It has just one small rack of new books, all more or less damaged because they don't actually fit in the rack... Do not expect a discount though, I tried! What I said, in case you're already on the station leaving for a long trip with the Shinkansen and just finished your book, you can go here for an emergency 'fix'.