Englishman or English man?

Solution 1:

Both "English man" and "Englishman" can be correct, but they mean (slightly) different things, and the latter is vastly more common. If you're speaking of a man from England (as opposed to a man from a different place), then the word you want is Englishman. If you're using English as an adjective, i.e. you've already established who this man is and you're adding additional description, then you can write it as two words.

If you have even a shred of doubt about which is correct, write it as one word.

Solution 2:

First of all, since group two is from a dictionary, one can generally assume it is more or less correct. I use group two; I believe it is correct, and Google Ngrams support this:
Englishman Ngram
Irishman Ngram
Scotsman Ngram
Welshman Ngram

Wikipedia's article on English people does not use "English man" once, but uses "Englishman" multiple times.

Wikipedia's article on Irish people does not use "Irish man" once, but uses "Irishman" eight times.

Wikipedia's article on Scottish people does not use "Scottish man" once, but "Scotsman" redirects to the page.

Finally, the article on Welsh people does not use "Welsh man" or "Welshman". However, the Free Dictionary has an entry for Welshman, but not "Welsh man".

I think we can safely assume that it is, in fact, group two.