In both British and American English, 'presently' can mean:

(1) In a short time: a bus will arrive presently; the sky grew dark and presently it started to rain. 

(2) At the present time: we are presently watching TV; my mother is presently in prison for drunkenness.

[Presently (etymonline)][1]  
[Presently (Oxford)][2]  
[Presently (Oxford Learners) ][3]

Meaning (1) is the majority usage in British English, although meaning (2) has been used since the 14th century, and meaning (2) is the majority usage in American English


  [1]: https://www.etymonline.com/word/presently
  [2]: https://en.oxforddictionaries.com/definition/presently
  [3]: https://www.oxfordlearnersdictionaries.com/definition/english/presently