Meaning of "presently" (US vs. UK)

“Usage note: presently. In both British English and North American English, presently can mean ‘soon’ or ‘after a short time’: I’ll be with you presently. In North American English the usual meaning of presently is ‘at the present time’ or ‘now’: She is presently living in Milan. ◇ There is presently no cure for the disease. This use is becoming more accepted in British English, but at present or currently are usually used.”¹

Presently has two meanings:

• In a little while (the usual meaning - both UK and US)

• Currently (less usual - mostly US)

However, there's rarely ambiguity, since the time contexts will differ between the two meanings. Together with a future sense, presently always has the meaning of in a little while (and both the UK and the US use it this way):

He will follow presently.

And when used with the present tense, presently always means currently (unusual in the UK):

He is presently in the dining room.

The moral: prefer at present or similar word/phrase to presently when you mean now. As the context of your quote says:

Clichés and jargon phrases tend to be wordy. ‘At this present moment in time’ is longer and less pleasant than either ‘now’ or ‘at present’. ‘Presently’ should be used with care until the Anglo-American difference of meaning has been resolved.

^{(Emphasis mine)}