Heathrow Connect was a train service in London provided jointly by Heathrow Express and Great Western Railway (GWR), between Heathrow Airport and Paddington Station. The service followed the same route as the non-stop Heathrow Express service but called at certain intermediate stations, connecting several locations in West London with each other, the airport, and Central London. It ran every half-hour throughout the day and evening. The service launched on 12 June 2005 and ran until 20 May 2018, when it was absorbed into the TfL Rail franchise, ahead of becoming part of the Elizabeth Line in autumn 2019.
More information on the Wikipedia page [1].
The website was https://www.heathrowconnect.com/index.asp?SID={4EA80D67-B12D-47C7-B63D-537636FAC7F6}