RELIABLE CAR SERVICE HEATROW TO HYATT CHURCHILL IN W1

Your best bet is just to get a metered taxi from the taxi rank outside the terminal.
This will be slower, and cost a lot more, than would taking the Heathrow Express to Paddington station and a taxi from there.
As you are going to a 5-star hotel I won't waste time even mentioning the cheap option (the tube).

It is not the customs which takes time, you just walk through the green "nothing to declare" channel; it is the passport and immigration check which occurs before you pick up your luggage. This is divided into *EU" and "non-EU". At Heathrow it can be 10-20 minute walk from the aircraft to passport control. Then the "non-EU" passport queue can be over 1 hour at busy times.

PLEASE DO NOT USE BLOCK CAPITALS AS IT SOUNDS LIKE YOU ARE SHOUTING.

Thanks Chis,
Sorry for the capitals . You could mention the cheaper options we really can't afford the cab. if there is a car service again,i am all for the tube but my husband does not want to deal with the stairs in train station. The hotel was a wedding present from relatives, we can't afford to even eat in the hotel. I'm more of a hostel b &b person. If you know of anywhere in that area that is not outrages for a meal that would be appreciated too.

Many people on this forum recommend Just Airports. They give a discount for paying cash.

OK, some boring details. There are basically 3 ways to get from Heathrow to central London.
1) Taxi. Not the fastest, definately the most expensive, but door-to-door.
2) Train (Heathrow Express or Heathrow connect. Not cheap. The business man's choice. Fast, no stairs at Heathrow or Paddington, but see below for details.
3) The Tube. London underground Piccadilly line. will get you within a "short walk" of your hotel. Cheap, slow (50 minutes), and you have to carry all your luggage. No stairs at Heathrow, but lots of stairs when you change lines and at your destination (Marble Arch station is nearest to your hotel).

Also, Heathrow is really 3 airports, you need to know which terminal are landing at.
"Heathrow Express" non-stop train, runs from terminal 5, and terminals 1-2-3, to Paddington station in 15 minutes for £21 single, £34 return. One train every 15 minutes
"Heathrow Connect", a slower train, runs from terminal 4, and terminals 1-2-3, to Paddington station in 27 minutes for £9.90 single. One train every 30 minutes.
But, you then need to get from Paddington station to your hotel. As this is not too far, and there is no direct tube connection, I would recommend a short taxi ride for first time travellers.

As an addendum to Chris F's post, I'd divide his first response:

1a: Taxi, meaning you get into an official taxi at the taxi rank at Heathrow.
1b: Car service, meaning a pre-booked car that you have arranged to pick you up.

Both give door-to-door service, but the car services are cheaper than getting a taxi at Heathrow. As posted above, Just Airports is often recommended, but there are others with good reputations. If you know for sure that you want door-to-door service, it's worth booking one in advance, for the savings.

Thank You for your responses. Is it difficult to hail a taxi for us to get to the hotel from paddington station? any idea what the cost would be for that ride? approx 3-4 miles.

Presuming there are just two of you, then the Heathrow Express is £25 round trip for each of you if booked in advance (Duo Saver).

There is a taxi rank at Paddington station, no need to try to hail them in the street. Fare should be in the £6-£8 range depending on any congestion. The distance is under 2km.

There is also a bus option from Paddington - the 36 or 436 to Marble Arch.