From what I can see there's Wizzair flights from Luton & there's also flights from Gatwick.

Hi Zonda.
Wizzair fly from London Luton to Kyiv Zhulyany (A basic airport to say the least),
Ukraine International fly from London Gatwick to Kyiv Boryspil (Ukraines main airport but much more basic than Manchester) and
British Airways fly London Heathrow to Kyiv Boryspil.
We flew a couple of weeks ago from Manchester via Heathrow to Boryspil and can thoroughly recommend flying with BA, although from November they change times from 09.50 to 08.00 making it impossible to fly from Manchester without an over night stop, so when we go again in December we will fly to Gatwick, have a few hours then fly with UIA to Boryspil, but we return with BA.

Alan