I will travel from Heathrow to central London, and was considering taking a taxi. My company will reimburse the taxi cost, however I need a receipt. Is it common to get a receipt after the taxi ride in London or should I explicitly ask the driver before the ride if he will be able to give one? I am not sure about this because in my country most drivers won't give you a receipt.
You will always be able to get a receipt. Drivers are used to people wanting to expense taxi rides, and will not be surprised by your request. Although there'd be no harm in asking up-front anyway.
It's usual to include the tip on the receipt itself - tell the driver to "make it up to (whatever the nearest £5 is)".
Note though that unless you're going at a very quiet time, a taxi to central London is unlikely to be quicker than taking the tube.