To help in playing chord progressions more smoothly, Doctor Uke has two simple PDFs with the most common progressions for three- & four- chord songs in all the main keys: I – IV – V7 & I – I7 – IV – V7. If you take these nice & slowly at first, paying attention to getting a good clean sound, then increase your speed gradually, you will build up good muscle memory of how to play these chords.
Also useful is the Ukulele For Dummies Chord Families sheet, which shows the basic chords for the main keys.
These three items make a nice warm-up at the start of your practice & can be varied by you changing the order of the chords or visiting the Doctor Uke’s Music Theory page, where he gives a number of songs in different keys for you to try.
Alternatively, you can add in practicing different strumming patterns whilst working through the chord progressions, with or without a metronome, to help you keep in time.