Heathrow express (HEX) have announced some discounted tickets for journeys in August http://-www.heathrowexpress.com/tickets-and-offers/book-early-to-save-money
There are 808 tickets available every day in August for £10 each (and even less if you have a railcard).
Most of us would say that the HEX is not worth the money for most visitors and even with the £10 fares I would say don't bother unless your destination is at or close to Paddington. But it is a lot better than the walk-up £25 fare and the advance £15 fares.