I would fly to Gatwick and catch the train to London victoria which is about a 30 min journey (either the standard train which is cheaper or the express which doesn’t stop but is slightly more expensive) then get a taxi to your hotel which won’t be far, or if you feel adventurous go for the tube which won’t cost more than a few pounds.
Getting the tube to central london from Heathrow is a real pain even during non rush hour times, and as said before taxi’s will need to be pre-booked from heathrow and are still very expensive.