本屋で英語関係の本を見つけると、次々に買ってしまって、読まずにいるので、たまる一方です。

、、、。

Whenever I find English-related books at the bookstore, I end up buying them one after another, and since I leave them unread, they just pile up.

Literal

Bookstore [at-で] English related-[attributive-の] books [object-を] find-[whenever-と], one-after-another buy-[regret-completion-てしまって], read-without-being [reason-ので], pile-up-[only-一方] [is-です].

A rich self-deprecating confession demonstrating several structures. ~と conditional expresses 'whenever/when' for habitual or inevitable results. 次々に ('one after another') is a common adverbial. 読まずに is the classical/literary negative te-form (~ずに = 'without doing'), less colloquial than 読まないで. ~一方だ ('only increases, gets more and more') is a set construction expressing a unidirectional trend — often about something spiraling out of control. A vivid, relatable sentence.