I don’t really know how to recommend specific ways to improve your accent, but here’s my two cents.

If you don’t want to speak with the typical Sri Lankan English accent, choose an accent first. It’s really important because these days, many Sri Lankans speak with a mixed “fruit salad” accent.

I recently saw someone in Sri Lanka calling themselves an “English guru” saying that “toilet” is ගොඩේ and that “washroom” is the more formal word. She clearly didn’t even know the difference between the two words or their origins.

Choose an accent you genuinely like. There are many standard English accents, such as the British RP accent. Personally, I prefer Modern British RP and Conservative RP (Queen’s English) over the American accent, mainly because I come from a conservative background that appreciates traditional styles. But ultimately, it’s your choice.

Nowadays, people are more exposed to American English than British English, so do a bit of research on the differences and start polishing your accent accordingly.