Synonymous with "exsqueeze me" (i.e. comical variant form of "excuse me") but even more casual. It's an acceptable contraction because in British English speech the formal "excuse me" will often be rattled off informally as "'scuse me"; and so "exsqueeze me" naturally becomes "squeeze me".
Simplifying "exsqueeze" to "squeeze" has a logical linguistic appeal because of the context in which the phrase is used. Typically if a speaker wants to say "excuse me" it is because their movement / passage is in some way being obstructed by another person (i.e. the person to whom the statement is addressed). By conjuring up the notion of a request to be squeezed the deviant form is therefore highly appropriate: the act of squeezing would necessarily result in a constriction, which would in turn facilitate the original request (i.e. by being squeezed the speaker would become smaller, and so the obstruction which forced him to make the request would become less problematic).
It sounds absurd, and yet it makes perfect sense. A beautiful tweak!
When shuffling past an attractive lady on a narrow aircraft gangway: "squeeze me"