He was interrupted before explaining further, but is he wrong? Wikipedia, and my memory, seems to insist that the British won... Anyone want to correct or support James?
(For those who are wondering, The Grand Tour is the spiritual successor to the original BBC Top Gear. You can watch it on Amazon Video.)
There are people who'd agree the Battle was a draw, not least Luftwaffe commanders and veterans; Eric 'Winkle' Brown interrogated Goering after the war who said it was a draw, Kesselring wrote that "To break off a battle that is going well is not by any means the same thing as being decisively defeated", James Holland interviewed surviving pilot Hans-Ekkehard Bob who "... still insists that the Luftwaffe did not lose the Battle of Britain, and prefers to think of it more as a draw". The overwhelming focus on and celebration of the RAF's Fighter Command can obscure a more holistic view of the summer of 1940, regular attempts to redress the balance sometimes stray a little far in diminishing Fighter Command's performance (even from its own veterans, notably the "indefatigably vituperative" H R 'Dizzy' Allen) or the significance of the Battle at all, arguing that the putative German invasion was merely a diversion to cover preparations for the attack on the Soviet Union; controversy could still stir up column inches 70 years on.
Certainly the Luftwaffe was not destroyed, so if the only criteria for victory is destruction of the enemy it couldn't be described in those terms, but preventing the Luftwaffe from achieving air superiority, forcing it to switch to night bombing, and causing the German invasion to be postponed and ultimately cancelled is generally seen as a victory for Britain (as a whole, not just the fighters of the RAF, though they made for good publicity both at home and overseas), critically forcing Germany into a two-front war, unable to focus its entire effort on the Soviet Union. Richard Overy, The Battle of Britain: "The contest was not, of course, a draw"; Stephen Bungay, Most Dangerous Enemy: "Victory in the air achieved a modest strategic goal, for it did not bring Britain any closer to victory in the war, but merely avoided her defeat"; James Holland, The Battle of Britain: "In 1940, Britain won the Battle of Britain, but she had not yet won the war". For a good overview of the portrayal of the Battle, both in its immediate aftermath and subsequently, Garry Campion's The Good Fight: Battle of Britain Propaganda and the Few is very good.