Hex is an open access operator it wasn't subject to franchising the first service between london Paddington and langley provided by london transport or its predecessor organisations was in 1883 tell me how many services ran to the airport then?
Oh dear, where to begin?
The station at Langley was opened by the Great Western Railway in 1845, some seven years after the GWR was opened and the station at Hayes (and Harlington) was opened around 1864. By no stretch of the imagination could the GWR be described as a predecessor organisation to the UndergrounD/LPTB/LTE/LTB/TfL etc.
What you may have in mind is the short-lived service run by the District Railway between Mansion House and Windsor between 1883 and 1885. In this sense the District Railway was a direct predecessor to TfL but it did not own the GWR's tracks.
You may want to think that HEx is an open access operator - but it is not. Open Access Operators are a creation of the Railways Act 1993 and the Heathrow Express rail link predates this Act, the Heathrow Express Railway Act of 1991. Acts of Parliament are not retrospective so HEx cannot be classified as 'open access'. I will point out again that BAA/HAL spent millions of its own money in building the track, tunnels and stations from the tunnel portal to the airport, this is not the modus operandi of subsequent Open Access operators working under the terms of the 1993 Act and this sets HEx apart.
I have also previously pointed out that if BAA/HAL had not built the Heathrow airport branch, then there would be no discussion at all about whether in the future Crossrail will be the death of HEx or not as Crossrail would have run only on the GWR's route to Slough, possibly Maidenhead, as there would not have been sufficient state funding to have built the Heathrow branch and stations as well as the central core tunnels.
To your last, rather bizarre, point: powered manned flight in heavier-than-air machines started with the Wright brothers on 17 December 1903. I can find no reference to an airport at Heathrow in 1883.