If you want to travel by rail into Central London, you have two options, both ending their journey at Paddington Station. Paddington is well connected by bus and the Underground for your ownward journey.
The Heathrow Express is a dedicated train line that runs every 15 minutes into London Paddington Station to the northwest of Central London. If you want to travel in style and get into Central London quickly then the Heathrow Express is your best option. It is more expensive than the Underground but much cheaper than a taxi and faster than both. Trains run non-stop between Heathrow and Paddington Station in Central London approximately four times per hour. Trains operate from about 5am until about midnight.
Time: From Heathrow Central (Terminals 1,2 and 3) it takes 15 minutes and from Terminal 5, 21 minutes.
Cost: £16.50 one-way
The Heathrow Connect is a newer service is a train that runs along the same route as the Heathrow Express to Paddington Station but with stops in Hayes, Shouthall, Hanwell, West Ealing, and Ealing Broadway along the way. If you will be staying anywhere in west London, this train makes more sense than heading all the way into Paddington Station and backtracking. Trains leave every 30 minutes from Terminal 4 and they take 25 minutes to Paddington with departures every half hour (every hour on Sundays). The Heathrow Connect train does not leave from Terminal 5. Trains operate from about 5am until about midnight.
Time: It takes 25 minutes to Paddington from Heathrow Central (Terminals 1,2 and 3)
Cost: £7.40 one-way