New PhD student here - what helped you to improve your academic writing?

Hi everyone, I’m a new PhD student who just got admitted yesterday (HUGE YAY). I am from non EU country, although I lived and studied in the UK, and I’d like to stay connected to the British/international academic community through publications and conferences.
One thing I’m struggling with is academic writing style. Ukrainian academic writing tends to be very formal and passive, while English-language papers often seem much more direct and natural. What helped you improve your academic writing the most?
Are there any books you’d genuinely recommend? And what are the main principles you follow when writing papers now — active vs passive voice, making claims, structuring arguments, etc.? I’d be especially interested in advice from people publishing in the UK, but any perspective is welcome.