Your other option is to take Heathrow Express to Paddington. It's a 15 min train ride and then a 15 min taxi ride. Alternatively, skip the taxi and you can take the tube from Paddington to Charing Cross or Embankment (also 10-15 mins).

If walking with luggage is a concern or if you don't want to deal with subway/crowds with your luggage, Heathrow Express/Taxi is your best combo. It's often the quickest as well, but also the most expensive.