If you want a short trip you don't want to take the Underground in from Heathrow. The Heathrow Express gets you to Paddington station in only ~15 minutes (vs. the better part of a crowded hour on the Underground), with train that run every 15 min. as well. You'll almost certainly be landing in the morning, which means you would be on the Piccadilly Line headed into central London at rush hour in a car that will be jammed to the gills with commuters. Not much fun with people tripping over you and your luggage. Take a look at:A direct route from Heathrow with as short a trip as possible ...
That's true, but because there are fewer people to transport on Sundays the Underground runs less often so the cars can still end up crowded.We arrive on a Sunday morning, commuter traffic should be lighter