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This is a known phenomenon also in Swedish where it is called _särskrivning_ ("writing apart"). The wikipedia article [Särskrivning](https://sv.wikipedia.org/wiki/S%C3%A4rskrivning) (Swedish, no English translation available) with sources claims that indeed the influence from English is to blame. The article also quotes a Dutch similar term  _Engelse ziekte_ ("English Disease", see the corresponding [Dutch wikipedia article](https://nl.wikipedia.org/wiki/Onjuist_spatiegebruik)), suggesting that this is also a problem in Dutch and likely in all of the Germanic languages.

The article also claims that in more recent times, wrong auto-correcting features from MS Word and similar are also to blame. But it also quotes Swedish examples from the 1700-1800s when influence from English was non-existent (but influence from French was significant). Although these examples predate a formalised grammar, which in Sweden didn't happen until the 19th century. So apparently in older times, there was no defined way of writing such words together or apart.

The wikipedia article also has an interesting remark about cursive writing, which was still taught in Swedish schools as late as the 1990s. A newer, more modern form of cursive writing was introduced during the 1970s with words and letters more apart, which could in turn indirectly lead to "writing apart" mistakes becoming more common.

Personally I don't think any particular influence is to blame - the cause is simply poor grammar knowledge of your own native language in general. Just the other day I were proofreading something with "writing apart" all over it and the person who wrote in barely knows English at all. To say that they did so because they were influenced by English would be ridiculous. They were simply illiterate in general. There is naturally a direct relation between poor grammar and people reading less books/articles in their native language. 

Similarly, people who speak a Germanic language often have problems writing English words together, when they shouldn't be. Just as I'm writing this very text, the English spell checker told me to change from "autocorrecting" to "auto-correcting".