There are those who are נוהג to wait until they get to shul before making a ברכה on washing their hands in the morning. When they get to shul, they then arrange the ברכה together with the rest of the morning ברכות [1], which are said in shul to be מוציא those who don't know how to make their own [2] ברכות (and even where there are no such people, nonetheless, there is no exception made [3]). [4]
The reason for this is because we don't make the other ברכות juxtaposed to washing our hands rather we leave them for where we get to shul, therefore the ברכה on washing hands also gets pushed off with them. ספרדים, on the other hand, hold that washing hands is no different than any other מצוה whose ברכה has to precede the מצוה, only that here one cannot make the ברכה before washing their hands because there is still רוח רעה on one's hands, to which end one should make the ברכה at the earliest opportunity, namely immediately following washing one's hands. The רמא himself (uncharacteristically) conducted himself like the ספרדים [5].
לבוש is singular among the אחרונים [6] to the effect that once עובר לעשייתן is not possible due to one's hands being unclean, there is therefore no preference at all to say the ברכה as soon as possible, but rather once it is pushed off it is then pushed off completely.
[1] שו"ע או"ח ו:ב. Additionally, there are those who wish to answer אמן to each other's ברכות, to which end they purposely say the ברכה later than they would have otherwise, in order to facilitate the saying of אמן to each other's ברכות. See שו"ת הרמע מפאנו סימן קט.
[2] ביהגר"א שם אות יב
[3] פרישה שם ס"ק ג
[4] According the בח (שם) this would only be allowed if one goes to shul right away, whereas if one engages in other tasks prior to going to shul then one must make the ברכה at home.
The בח seems to assume that if one goes straight to shul then that is already some form of עובר לעשייתן, whereas engaging in other tasks prior to that would be considered a הפסק גמור. This point, however, is not entirely clear from the בח itself but rather constitutes my own attempt to fill in the blank.
[5] טז שם ס"ק ד
[6] או"ח שם סעיף ב