The very cheapest way for you to get from Heathrow to the Mayfair InterContinental would have been the tube: the Piccadilly line runs from Heathrow through Green Park station (among others) The InterContinental is around the corner (about 100m) from Green Park station.
Probably not a great idea if you have much luggage, though... and definitely avoid the Piccadilly line during rush hour.