Quick answers

I used the Plan a Journey search and there are trains on the Piccadilly line leaving from Terminal 5 at 22:44, 22:54 and 23:14 and then change to the District line at Hammersmith and alight at Westminster and cross the bridge to get to your hotel. http://www.tfl.gov.uk/plan-a-journey/

Many taxis do take credit cards. You should ask before you get in.

Or take a car service.

A pre-booked car service would be cheaper than a taxi from the rank.

I've arrived around 10pm several times and getting off the plane, picking up luggage, and getting through passport control always took an hour or so.

That's cutting too close to the last Tube departure for me. And, if the flight's late...

I've taken the Tube in at that time of night (not my favorite), as well as the Heathrow Express (from Terminal 5, last train at 23:42 currently), taken a taxi and booked a car.

I'd recommend booking a car service. Costs more but gets you straight to the hotel (in about an hour).

I'd also arrive prepared to spring for a taxi if I had no other choice. I buy 100 pounds or so at my U.S. departure airport just in case.

Thanks for your answers and taking the time to reply. Note will be quick as it's going on 11 p.m.here..This was a good reminder for us to have a plan B and note the opening and closing hours. We'd planned for an a.m.arrival and ended up with a Really late p.m.arrival. Weren't off the original flight and re-booking until 1a.m. And on to new one at 8:15 a.m. I'll write more later, but able to catch last Heathrow express at 11:48pm then taxi from Paddington. What a journey!

On the flip side, stories for the future and it's great to be in London,
Patty

Patty, I've taken the United flight out of IAD that arrives at 10pm at least half a dozen times. Only once did I arrive too late to make the tube and that was because the flight departed 3 hours late. Every other time, I've made the tube well before the last departure. Unless your flight is exceptionally late, you should be fine on the tube. The last couple times, I've zipped through immigration and been on the tube within 30 minutes of wheels down.

You can check the journey planner on tfl.gov.uk to see when the latest tube leaves.

Sorry, just saw your note that you arrived and made the HEX. Glad you made it.

Glad to hear you made it! Have a great visit!!!