The word directly, of course, is found in both AmE and BrE, as in:
Try to involve everyone, not just those directly in front of you. [University of Kent Careers Advisory Service, Tips on Making Presentations]But the use of directly to mean 'shortly' or 'very soon', is mostly AmE--though the OED indicates that it's also BrE dialectal (but which dialects? do you know?). It's that sense of the word that's used when a (AmE) salesclerk/(BrE) shop assistant says:
I'll be with you directly....before they ignore you in order to deal with another customer.
For this meaning, shortly works in BrE (as well as AmE), but when I asked Better Half what he'd say instead of I'll do that directly, he said that he'd say I'll do that later. When I countered that that doesn't mean the same thing, he claimed that as a British person, he was less likely than an American to want to tie himself down to anything more specific. I think he was joking (he's rarely not joking), but if you'd like to protest or support his contention, feel free to do so in the comments!
Afterthought (the next morning): A good South African equivalent is just now, which confused (or maybe annoyed) me to no end when I first arrived there and went to a party with a co-worker. He kept saying We'll leave just now and so I'd fetched my bag or whatever and found myself waiting while he drank another drink, and another, and had another conversation...
Note that the dialectal differences involving directly and just now are not about whether they are used to talk about time, which they generally are in a lot of dialects, but whether they're used to mean 'not immediately, but soonish', which tends to be more dialect-specific. Just now in my native AmE dialect can mean 'in the very recent past' and directly can mean 'immediately' in most dialects.