How long will it take me to get from Covent Garden to Heathrow Terminal 5 on a weekday evening?
I'm planning to take the Tube from Covent Garden to Paddington Station and Heathrow Express from there.
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To find a specific answer, your best bet is to use the TFL Journey Planner. Tell it exactly when you want to leave, how fast your walk, if you want to minimise walking and/or changes (eg due to baggage), and it'll give you an answer
In general through, from Covent Garden to Heathrow, there are two options. One is slightly quicker, one is a lot cheaper.
Option one - board a Heathrow bound Piccadilly Line train. There's roughly one every 7 minutes for most of the day. Take that all the way to Heathrow, should take just under an hour (50-55 minutes once your onboard). Then, walk to your terminal, allow about 10 minutes. It's a zone 1 - zone 6 single, unless you have a travel card. Using an Oyster card, off-peak it's £3 for the journey.
Alternately, make your way to Paddington Station, then take the Heathrow Express. From Paddington there's 4 trains an hour, journey time of about 15 minutes to T1/T2/T3, 20 minutes to T5, absolute age to T4 because you have to change.... From Covent Garden to Paddington, there's two options. You can either take a Piccadilly Line train to Piccadilly Circus and change to Bakerloo line. Or, if you don't have too much luggage, enjoy a pleasant 10 minute walk from Covent Garden down to Charring Cross, then 10 minutes on the Bakerloo up to Paddington. I'd say that with changes and waits for trains, allow about 30-35 minutes either way from Covent Garden to being at the Heathrow Express platform in Paddington. As such, the Heathrow Express option isn't looking much quicker, but is looking about £20 more expensive!
I have an app called Tube Map on my phone and it says Covent Garden to Paddington is 19 minutes. Seven stops, two lines - Piccadilly line to Piccadilly Circus, change to Bakerloo Line to Paddington. It's about 6:40 pm in the UK now so if the app takes time of day into account, it's the right time. There appear to be trains on both lines about every 2 or 3 minutes at this time of day.
Allow ten minutes for getting from the tube to the Heathrow Express platform.
There's a train every 15 minutes, so worse case you would just miss one and wait 15 minutes for the next. The travel time is 15 minutes.
So all told: 59 minutes. Call it one hour. Then you have to get to your terminal from the Heathrow Express station, but that's a different question :-)