The reason for denial was because you are considered a high risk for overstay due to your indefinite leave in UK and Ukrainian Citizenship (the US wants you to apply from your fixed, permanent place of residence and that both countries be stable - Ukraine is not in the East, right now). As such, you were denied under 214(b) - the suspicion that you would overstay your visa if granted.
ONCE you have UK citizenship, the US is much more likely to allow a visa. This includes ESTA/VWP, since you would not longer be considered an overstay risk, likely.
NOTE, that ESTA/VWP is more or less all automated. Any little thing can make ESTA deny, so there is still a chance that you may be denied ESTA with a UK Citizenship given your overall history. But a B1/B2 visa (or whatever else) would be likely granted once UK Citizenship is established.
As they say: "Щасти!"
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