The airlines get almost no internal subsidy whilst the trains are awarded generous subsidy through Network Rail to upgrade large sections of the railway network.
The domestic airline business gets a larger subsidy than the rail network through duty free fuel.  I forget the exact numbers but the missing ~50p per litre tax on fuel amounts of a subsidy of some £7bn a year or just a little more than the rail network's subsidy.
Do the UK railroads pay duty on their fuel (on the non-electrified sections) and on their electricity on the electrified sections ?

I am not sure that the absence of a tax is a subsidy per se.

Alan

"Do the UK railroads pay duty on their fuel (on the non-electrified sections) and on their electricity on the electrified sections ?"

There is a small excise duty payable on railway gasoil, similar to that levied on home heating oil.  It is nowhere near the duty levied on road vehicle fuel in the UK, but the railways pay directly for their right of way, whereas road vehicles do not.

sf

One also has to look at the cost of building, operating and maintaining airports (including the cost of 1000s of acres of land), navaids, ATC services, etc.  I don't know the situation in the U.K. and don't have the time to research it at the moment.

I know that in Canada the cost of ATC services alone was over $400 million per year about 15 years ago.  That's a pretty damn hefty direct government subsidy - $13 for every man, woman and child in Canada, just for ATC, whether they set foot on a plane or not.  The service is now run by NAV Canada, a "non-share capital, private corporation" which recovers costs from aircraft operators.  i.e. the government subsidy is now gone.  The cost of flying has, not surprisingly, increased substantially.  Canadian registered aircraft in the range 2 to 3 metric tonne maximum takeoff weight (4400-6600 pounds) pay $236/year.  The daily charge for a DHC-8-400 (as an example, as it cropped up above) is $2441.

http://navcanada.ca/ContentDefinitionFiles/Services/ChargesAndAdmin/guidetocharges/Customer_Guide_Ne w_en.pdf

I believe in the UK the airlines pay a surcharge to the airport.   I believe UK airports are profit making, tax paying businesses.  As far as I know they are not part of any government organisation and do not recieve direct subsidy other than any local tax breaks they can negotiate with local authorities.  

Pretty much the same as any other large industry.