Cable thickness for solar borehole pump
The question is really whether it is worth transforming that power up to 240V to cover the distance.

You can establish the feasibility of 24V transmission using Ohm's Law :

This page gives the resistance of 2000 feet of 8awg (10mm^2) wire as approaching 1.5 ohms. At 10 amps, that implies a drop of 15v leaving only 9v to run the pump. 

Now, price out 2000ft of 8awg ... I'm seeing £130 for 100m in 5 or more, or about £650 for the length you need. You can probably do better but thicker wire would be more expensive...
I think you can probably afford a 240V inverter for that sort of money, and save money on cable as well as reducing I^2R losses.

To flesh that out a little, at 1 amp those 8awg cables would drop 1.5 volts : that's less than 1% of your 240V supply. So use thinner cables; lose 10V (4%) or so but you'll lose maybe 10% in the inverter anyway. The reduced price of the thinner cables will pay for the inverter. This is looking like a better solution.