I am not a linguist in any sense, but the answer appears to be that English has no unique traits (excluding trivial "features")*. From both a spoken and written perspective, English was formed as a mix of other languages. There is nothing that I'm aware of—grammatically, phonetically, or conceptually—that can be expressed solely in English.
Here are some possibilities that stand out in English (from comments):
- English stands out as one of about a dozen languages to use "we" as "I" (the Royal "we" / Majestic plural), though it's not unique. – Zairja
- Not unique as per comment: I remember that in one of his books (probably « la structure des langues »), Hagège mentioned that constructions à la “Do you know what I'm thinking about?“ with this separation between the preposition and the conjunction were very original. I will try to find what he says exactly and post it as an answer. – JPP
- "Did" at the beginning of this sentence has no meaning. That's a feature caused English being filtered through Celtic language speakers. Their feature came out as a "do" as in "Do you have a car?" which would be rendered as "Vous avez une voiture?" in French, literally "You have a car?" – Nick Anderegg, (Do-support - though there seems to be some controversy between grammarians and linguists)
Additional traits might be gleaned from these published works, but I could only preview some of them (no university access at the moment).
*A trivial feature would be, for example, no language spells "horse" like English.