https://www.heathrowexpress.com/tickets-deals/prices-fares

Book at least 90, 30 or 7 days in advance for savings of 65%, 50% or 25%
compared to the regular price (i.e. purchased online or from ticket
office or ticket machine).

HEx Advance Tickets are valid for travel at any time of day on the
booked date - for return Advance tickets, the return portion is valid up
to a month after the outward journey.

They are only issued as e-tickets (email to print at home/office) or
m-tickets (mobile/smartphone).