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My wife has done this particular one several times.
And you will be going through passport control in Kyiv at arrival from London.
But if you prefer you can look at the site of Borispyl's airport site:
If you arrive at Boryspil airport by international flight and proceed to the domestic departure you donβt have to claim your baggage.
After you pass through immigration control you should proceed through Arrival Hall and customs control area to escalator, then go up to the second level to the domestic area for check-in (if needed) and aviation security control.
If you have items to be declared in your baggage you should claim it. In that case during the check-in at the airport of departure please, notify in advance to check-in your baggage only to Boryspil airport. If baggage was checked-in to final destination notify hostess at the International Arrival Hall that you need to claim your baggage