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Not quite. Heathrow normally operates with one runway closed until 06:00 - that's when dual runway arrivals start.
There are only around 15 flights scheduled/allowed to land from 04:30 to 06:00, so one runway is more than adequate during that period."
This is to allow for longhaul overnight arrivals.
AFAIK (but stand to be corrected!), no departures are allowed before 0600.