What time do Heathrow taxis start running?

There isn't a start time. Taxis to Heathrow run 24 hours a day, every day of the year, because flights don't stop at midnight and neither does the demand for a lift to catch them.

What genuinely changes overnight is not availability but traffic. Between roughly 1am and 5am, the M4 and the roads through Slough and Colnbrook are close to empty, so a 3am pickup from Maidenhead can reach Terminal 5 in under 25 minutes — a journey that might take 40 in Friday rush hour. If your flight has a 4:30am check-in cutoff, an early pickup is usually the safer bet, not because a car won't be there, but because you'd rather have slack in hand than none.

Booking an early or late pickup

The one thing that matters more overnight than during the day is giving a real flight number when you book, not just a pickup time. Flight numbers let a driver check actual departure and adjust the collection time if your flight has moved — useful for the 6am departures that get brought forward as much as delayed. Book the night before if you can, simply so the driver has your details locked in before they start their shift.

Terminal drop-off at odd hours

Heathrow's terminal forecourts are staffed and lit at all hours, and drop-off works exactly the same at 3am as it does at 3pm — pull up, bags out, gone. The only practical difference is that security queues at Terminal 5 tend to be shorter before 5am, which is one more reason an early pickup for a 6am or 7am flight is usually worth it even if it feels aggressively early when your alarm goes off.

What about picking someone up from an overnight arrival?

Same answer: the car is there. Give the flight number, and pickup adjusts to actual landing time rather than the scheduled one, so you are not sitting in an empty arrivals hall at 2am waiting on a flight that landed at 1:40.

If you've got an odd-hours flight from Burnham, Slough, Windsor, Maidenhead or Marlow, the practical advice is the same regardless of the hour: book ahead, give the flight number, and call rather than message if it's inside a two-hour window — a live person confirming a 3am car is worth more than a form.