A large part of it came down to aesthetics. The Spitfire is an exceptionally good-looking aircraft, in my opinion probably one of the most beautiful aircraft ever made. The Hurricane on the other hand, was a rather pedestrian-looking design. Serviceable, but somewhat dumpy.

So when it came time to film aircraft for newsreels and propaganda, the Spitfire became the "face" of Fighter Command.

I'd imagine it'd have something to do with the fact that at the time it was considered one of the most advanced planes in the world, on par with the BF109.

That said, it might have been a deliberate propaganda movement but Spitfires (the MkIs) were used (albiet far less than the hurricanes) pretty extensively in the BoB.

From what I recall from my reading of the Battle of Britain, the Spitfires were a touch faster, arguably more recognizable because of the fact that there were quite a few privately owned Spitfires. But this is mainly postulation. In the actual battle itself, the Hawker Hurricane would prove to be much more effective partially because it was a much simpler machine to service and refuel wheras repairs on a Spitfire tended to take longer. Although the Spitfire performed well, the Hawker's cheaper construction meant turn around times allowed it to be in the field more.

Even though it was a slower plane, both shared the 8x Browning .303 Machine gun armnament generally. So the answer to your question would probably lie somewhere between the Spitfire being a newer plane at the time, its popularity in the fact that it was a very advanced fighter, and that the Spitfire was continually upgraded and improved through the war and fondly remembered for the later much more powerful iterations.

The Spitfire, as mentioned, is generally regarded as an extremely good looking aircraft, and "... handled like a thoroughbred from the start, and its performance staggered everybody who saw it demonstrated" (Thetford, Owen Aircraft of the RAF Since 1918). It was a superb fighter, in production from the first day of war until the last (albeit with substantial modifications over time), in service with the RAF until 1951.

The Hurricane was a fine fighter, but the advantages it offered over the Spitfire were distinctly "unsexy", if you'll forgive the term. Simpler production methods meant there were more of them, ease of maintenance kept them flying, and pilots admired their ruggedness and stability as a gun platform. Wing Commander Robert Stanford Tuck:

"My first reaction wasn’t good. After the Spit, she [the Hurricane] was like a flying brick – a great, lumbering farmyard stallion compared with a dainty and gentle thoroughbred. The Spit was so much smaller, sleeker, smoother – and a bit faster too. It nearly broke my heart, because things seemed tough enough without having to take on 109s in a heavy great kite like this.

But after the first few minutes I began to realize the Hurri had virtues of her own. She was solid, obviously able to stand up to an awful lot of punishment . . . steady as a rock – a wonderful gun platform . . . just as well powered as any other fighter in the world, with the same Merlin I knew and trusted so well.

The pilot’s visibility was considerably better than in the Spit, because the nose sloped downwards more steeply from the cockpit to the spinner. This, of course, gave much better shooting conditions. The undercart was wider and, I think, stronger than the Spit’s. This made landing a lot less tricky, particularly on rough ground. The controls were much heavier and it took a lot more muscle to haul her around the sky – and yet, you know, after that first hop, after I’d got the feel of her, I never seemed to notice this, or any of the other differences any more."

(Stewart, Adrian They Flew Hurricanes)

'Spitfire snobbery' was even present in the Luftwaffe at the time:

"The Jäger [fighter pilots] of the Luftwaffe did not think the Hurricane was much good. This may have been partly because they often mistook Hurricanes for Spitfires. Both Kesselring [head of Luftflotte – Air Fleet – 2 in the Battle of France and Battle of Britain] and Osterkamp [his fighter commander] fell into the trap . ‘Uncle Theo’ ‘saw’ Spitfires on the ground in the Battle of France; Kesselring said, ‘Only the Spitfires worried us.’ Both were wrong. There were no Spitfires in France and in the Battle of Britain they shot down, in the aggregate, fewer than the Hurricanes." (ibid)

To employ a sporting metaphor you could liken Hurricanes to the pack of forwards in rugby or offensive linemen in the NFL, and Spitfires to the try-scoring winger or quarterback; the former are essential but often unsung heroes, while the latter tend to pick up the headlines.