Probably between 70 GBP to well over 100 GBP.
Your're much better off financially using a prepaid transfer car like UBER.

Also, the new Elizabeth line will take you directly (and pretty fast) from LHR to Bond street station, and from there a black cab to the hotel will be no more than 20 GBP at most. All central London Elizabeth line stations are new and have both escalators end elevators from platform to street level, unlike the older, much smaller, and much less practical tube stations on the Piccadilly line.