The test to distinguish a 
> [`Verb` + `[Prepositional Phrase]`] 

constituent from a 
> [`[Phrasal Verb]` + `Object`] 

constituent uses the syntactic rule of [Particle Shift, which applies only to phrasal verbs][1].

The test works like this: true transitive phrasal verbs like *look up* in its 'research' sense govern  the syntactic alternation that produces these two synonymous grammatical sentences:

 - *I **looked up** the word in a dictionary.*
 - *I **looked** the word **up** in a dictionary.*

The "particle" (which is a question-begging term for the "preposition part" of a phrasal verb)  
may appear either **before** or **after** the direct object noun phrase, at the speaker's choice.  
There is no difference except pronunciation between these two variants.  Further examples:

 - *They **burned up/down** the barn. ~ They **burned** the barn **up/down**.*
 - *She **drank up/down** her coffee. ~  She **drank** her coffee **up/down**.* 

By comparison, real prepositional phrases do not allow the object to appear before the preposition:

 - *He looked up the staircase,* but not *_He looked the staircase up._

Applying this test to the original example phrases, we find that 

 - *The ivy is creeping up the backstairs*, but not *_The ivy is creeping the backstairs up._
 - *The ivy is climbing up the wall,* but not *_The ivy is climbing the wall up._

So the syntax lab results show that these are **not** phrasal verbs (because they fail the test),  
but rather verbs modified by prepositional phrases.

The situation is even more definitive with a pronoun object; phrasal verbs **require** Particle Shift 
with pronoun objects, so we get very clear contrasts like

 - *That's the dictionary I looked it up in* ~ *_That's the dictionary I looked up it in._  
but
 - *_The back wall, the ivy is climbing it up_ ~ *The back wall, the ivy is climbing up it.*

  [1]: http://www.umich.edu/~jlawler/EnglishPhrasalVerbs.pdf