Unfortunately there is no real budget option for longer focal length than 300mm. There are some 500mm mirror lenses about, but they really are pants, although for most aviation you do not really have to worry about the donut bokeh. They are soft and very low contrast with a lot of vignet. Even with good PP the results are very disappointing. Forget about using a 1.4× or 2× converter, as AF will not be working at those apertures. So it's MF only and that is really hard on an AF lens, as the throws are so short. Also infinity focus is before the end stop to prevent damage to the AF drive systems
Aside from those then really you are looking at the 100-400 L MK I. I guess they are now available new at around/under £1000 now the MK II is out. The Tamron 150-600 looks really good for the money, but be aware the VC system won't work while panning, so slow shutter speeds for good prop blur are difficult. The Sigma 150-600 is good but the price is high. I would guess that the old 150-500 OS would probably be the cheapest buy, but that is till going to be around £500.
Alan