What is the best and most economical way to get from Heathrow to downtown London when we arrive on Christmas Day?
If you have any chance to change your flight without a big financial hit, don't fly into London on Christmas Day. There is NO public transport in London on Christmas Day. Last year there was a limited coach service from Heathrow to Central London but there's no guarantees that there will be this year. Also central London is quite big and you might still have a distance to reach your hotel. Otherwise you're limited to taxis or pre-booked shuttle services. They will charge punitive rates for travel on Christmas Day since there are no alternatives. If you're planning to hire a car later in your holiday, it might even be best to do that at the airport and park it somewhere in London until you leave. But the "best and most economical way" will probably be not to attempt to travel on that date.
What Philip says. I was going to cheekily suggest: best - ridiculously priced taxi
cheapest - walk but I see he has beaten me to it. On Christmas Day, really don't count on anything. On Boxing Day the buses and tubes are back but still no trains.
Hotel by bus, which is a shared bus ride into London quotes £22.50 per person on Christmas Day. However, I'd check things out with them as they may well have forgotten to block the day off.
A private car service will be much cheaper than a taxi. Many people recommend Just Airports. There is a discount for paying cash.
The Oxford Tube which normally runs services to both Heathrow and Central London will be running hourly on Christmas Day as a combined Oxford->Heathrow->London as in previous years. However, they are not at present offering a fare between Heathrow and London this year. Having looked at the timetable Oxford is unusual in having two intra-city buses running on 25 Dec - effectively these are night bus services running all day.
Also the Underground shuts down early Christmas Eve so the rolling stock can get back to where it needs to be in order to resume services after the holidays.
I am arriving on Christmas Day and have been searching for transport from Heathrow to London. I found 2 taxi companies to be quite reasonable. http://www.247airporttransfer.co.uk/ They charge 50% more for Christmas Day but their normal price is ok anyway. The other one is https://www.airporttaxis-uk.co.uk/ which lets you book online without adding 50% but not sure if they will add it later in the booking.