At present the GWR Preservation Group occasionally runs steam trains along sidings at the Southall Railway Centre.
Next year it will begin carrying passengers over the full three miles of the Brentford branch line.
But, despite the delights of passing under Brunel's famous Three Bridges near Hanwell, passengers will have to stay in their carriages when they reach the southern end of the line because there is no station there.
Funding is needed to pay for platforms to be built near Transport Avenue in Brentford. Once they are in place, passengers will be able to alight and visit notable west London landmarks such as Chiswick House, the Royal Botanic Gardens at Kew and the Steam Museum. They would complete their round-trip by coach or by a return journey on the train.
The GWR group, which has nine locomotives on display at its centre in Southall, alongside the main InterCity line from Paddington to the West Country, believes the station would provide a worthwhile tourist and educational facility.
Steam enthusiast Bob Gorringe said the station was bound to bring more visitors to this part of west London.
'This would be very good for us and for people who want to come and see the various sites around here and travel by steam railway.
'It is quite a rare opportunity because this will be the first working steam railway in London,' he said.
Day-trippers would also be able to visit Hounslow's lesser known treasures such as the Watermans Arts Centre, which sits on the north bank of
the Thames looking across towards Kew, and the Musical Museum, which holds one of the world's largest collections of automated instruments.
The money for the station project is being sought from the Government by Hounslow council which has asked for pounds 22m for the rejuvenation of Brentford. The scheme will include a housing programme and an initiative to combat crime as well as the building of the station.
Nigel Horton-Baker, the council's community and economic development chief, said: 'We already have a train tour operator interested and Railtrack seem to be quite happy about it too,' he said.
Steam trains served the capital for almost 140 years since the start of the London and Greenwich railway in 1830. However, by the Sixties steam in London was in decline. Services ceased from King's Cross in 1963 and from Euston a year later, and the final regular steam-run service to go was out of Waterloo. It last ran in 1967.