Before I read Craig Shrives grammar book I would always write, 'into' when writing a sentence with 'into' in it. Recently, I sent an email with, 'in to' used twice. Is it, 'into' or 'in to'?
It's a house that's been divided in to two separate flats, I'm on the upper floor. There is one flight of stairs to take in to consideration.
...divided into two separate flats... one flight of stairs to take into consideration.
The other 'preposition', 'in to'....actually...doesn't exist, because it's 'in + infinitive'.
I went in to buy a newspaper.
My grammar should be improving after reading Craig Shrives, Grammar Rules, book. Both 'into's' were wrong.
"Into" is the correct form in your examples. But there's more to this than you may think, since both forms can occur as prepositions, though with different meanings.
INTO as a compound preposition:
(1) "Ed fell into the pool".
(2) "The frog turned into a handsome prince".
(3) "The accident happened three weeks into the vacation".
"Into" can indicate movement towards the inside of a place as in (1). It can also indicate a change of state, as in (2). And it can have a temporal meaning, as in (3). Those are just three uses; for more see here: http://dictionary.cambridge.org/dictionary/learner-english/into
IN TO as separate prepositions:
(4) "Kim would not give in to her demands".
(5) "He gave in to the pressure".
(6) "Ed handed his paper in to the teacher".
The composite form has a number of different uses, as can be seen in (4) and (5), where "give in to" is a verbal idiom meaning 'succumb', and (6) where "in to" indicates movement and transfer of something to a recipient.
Now consider your two examples:
(7) "It's a house that's been divided in to into two separate flats".
(8) "There is one flight of stairs to take in to into consideration".
In (7) a change of state is indicated, just as in (2), so the compound "into" is correct. And (8), an idiom, means to take into account, and again the compound form "into" is correct.
(1) traditional grammar treats the "in" seen in examples (4) - (6) as an adverb, but modern grammar analyses it as a preposition.
(2) the "to" that is used to introduce infinitival verb phrases, as in "Ed just popped in to check on something", is a subordinator, not a preposition.