This is the picking/strum pattern I use to play Want You Gone. See here for chords/lyrics. See Youtube for my ukulele play-along video.

I use 2 picking/strum patterns in different sections of the song:

1. Picking - verse
2. Rock strum - verse, chorus

The finger-string assignment is:

1. G - thumb
2. C - index
3. E - middle

1. Picking - verse

In order to sound like the original, you will need a ukulele with a low G string.

The picking pattern here is different for each of the chords: Bbsus#4, Ebm. Since you don't play the A string, you don't need to hold down a fret there.

    Bbsus#4   Ebm
  A|------------------
  E|--1-1------------2-
  C|-------4----3-3---
  G|-3-3--3----3-3--3--
  

For Bbsus#4, hold down the chord shape 341x. The picking pattern is thumb - middle - thumb - middle, thumb - index.

For Ebm, hold down the chord shape 332x. The picking pattern is thumb - index, thumb - index, thumb - middle.

In each verse, there are 2 points where you don't finish the entire Ebm picking pattern. In the Ebm => F transition, pick the first 4 notes of the Ebm picking pattern, and then switch to a strum for the F chord. Similarly in the Ebm => D, G (transition from verse to chorus), pick the first 4 notes, and then switch to a strum for the D and G chords. The strum pattern used is the rock strum, which I'll describe in the next section.

2. Rock strum - verse, chorus

The strum pattern used for the verse and chorus is the rock strum. A rock strum is characterized by an emphasis on the third beat. The verse and most of the chorus uses the basic rock strum.

  1 2 3 4
  d   D du
  

For the Bm => C transition in the chorus, I play an extended rock strum. You can substitute the regular rock strum here. The extended rock strum I play is:

  Bm     C
  1+2+3+4+1+2+3+4+
  d   D du ud D du