My colleague and I are in constant debate about the use of onto. For example, if I write "I climbed onto the table" is this correct or should I write "on to"?
Please put us out of our misery.
"if I write "I climbed onto the table" is this correct"
YES you are quite right, because the verb "climb" is a verb which implies 'movement'
Into and onto are used with (some kind of) motion whereas in and on are used when the situation is static.
I went into the room. I stayed in the room for 3 hours. - or at least, that's the rule, but it's not always used. (Instead of "Put the glass onto the table", you will hear "Put the glass on the table")
Not to be confused with the "on" which is part of a phrasal verb as in "carry on". Example: "we went to London and then we went to Birmingham" = "We went to London and then we carried on to Birmingham"