The rule for a OWE stopover reads:

152N . 1. A STOPOVER IS A BREAK OF JOURNEY OVER 24 HOURS.

My planned flight arrives at LHR at 21:30, and I want to connect with another that departs LHR at 21:30 the following day.

The way I see it that's 24 hours exactly (not over) so it should be allowed as a transit. Will the airlines agree?