Heathrow Express is offering a "fixed date off-peak" special Fare of £15 for tickets bought online more than 24 hours in advance. Tickets must be purchased by 23 April for use by 21 May, and are only good during off-peak hours ( basically 10 am to 4pm). They are good for travel in either direction.
https://www.heathrowexpress.com/tickets-deals/prices-fares
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