Minicab from the hotel to Paddington at 6:15am, plenty of time for the 6:40 Heathrow Express changing at Heathrow Central arriving at 7:15. No stress, no fuss, no hugely unreliable Piccadilly Line (). Shop around for a HEX discount voucher, cab will be GBP10.

Which hotel are you at? The Holiday Inn Express Swiss Cottage? If so, tube to Paddington is an option as the hotel is 100 yards from the tube.