While it may not be widely promoted, Heathrow Express actually offers group discounts for groups of four or more. Unlike most of their promotions which can only be booked online, this offer can actually only be booked at a Heathrow Express Ticket Office at Paddington or Heathrow Airport.
This discount is only available on Saturdays, Sundays and Bank Holidays for groups of four or more and is for express class single tickets. Depending on whether there are current other offers from Heathrow Express you might be able to find a better deal, but certainly keep this option in mind, as you can save 50% per person, a total savings of £33.00 for a group of four.
Visit the Heathrow Express website for more details.