In all the visits we've made to London we have never been able to justify the cost of Heathrow Express over the alternate methods. The time savings is there, but not enough to make up for the significant additional cost. I agree with the other posters who have recommended the Elizabeth Line as the best alternative. We usually just buy day Travelcards, ride the Elizabeth Line into the city centre and then use our Travelcards on the Tube for the rest of the day.