Planning on staying at the Grand Royal Shaftesbury Hotel.
What is the fastest and cheapest way to Heathrow?
What would a private car cost?
What is the tube route?
Thanks

Are you incapable of (1) reading a tube map, (2) googling car services for London, or (3) searching these forums -- it's not like this question (transport to LHR) didn't occur to others. If you told folks where the hotel was instead of having us look it up and figure out where you're going from to get to LHR, it would be easier.

Ultimately, "the fastest" and "the cheapest" are separate options.

Big Russ said it all.

You are arriving at St Pancras and leaving from LHR -and have chosen a hotel near Queensway Tube?

That location is not at all convenient from/to either end of your journey and is not convenient to most sights. In fact it is a slog from both St Pancras and lHR.

Just get a car service (or even better, IMO change hotels)

justairports.com

The best way to LHR from the Hyde Park area depends a bit on the side of park you are on. As a rule of thumb North of Hyde Park, it's likely to be quickest to go to Paddington and get the LHR Connect or LHR Express (quicker and more expensive than Connect) train.
South of Hyde Park, just get onto the Piccadilly Line (Hyde Park Corner, Knightsbridge, South Kensington stops) which takes about 45 min. to LHR nonstop.

And if you are arriving at St Pancras and leaving from LHR staying in Queensway is not the best of ideas as it's a hassle to get to & from from either St Pancras or LHR.

If you have an early early morning flight then stay near Paddington to get the early early HEX, otherwise just stay somewhere like Bloomsbury, South Kensington or Earls Court which have direct connections to both St Pancras & LHR

"<i>depends a bit on the side of park you are on. As a rule of thumb North of Hyde Park it's likely to be quickest to go to Paddington and get the LHR Connect or LHR Express . . . .
South of Hyde Park, just get onto the Piccadilly Line </i>"

True enough - however we know exactly where the OP is staying. Their hotel is just around the corner from Queensway tube station. But even being north of the park - a car service will be cheaper and easier than getting to Paddington and then catching a train to LHR.

this is why I chose this hotel" Grand Royale London Hyde Park is located in Paddington adjacent to Hyde Park and Notthing Hill whilst being surrounded by all the excitement of London's West End and where our guests can expect to. The newest luxury property in London is located close to major transport links and within easy reach of Heathrow Airport, making it an attractive proposition for frequent fliers and business travelers. "
from Shaftesbury hotel website.

"True enough - however we know exactly where the OP is staying. [...] But even being north of the park - a car service will be cheaper and easier than getting to Paddington and then catching a train to LHR."

1. Thanks for the appreciation.
2. I could not be bothered to look up the location of a hotel the name of which is not even exact, which is why I gave a valid rule of thumb.
3. The OP never stated that he/she needs to get to LHR from the hotel - only from the Hyde Park area.
4. If the OP is traveling single, a car service may be easier, but not necessarily cheaper. The maths for a car service normally work only if there is more than 1 passenger.
5. Overall at least my post was answered the question without judging its validity.