As for British jets, the answer is pretty straightforward: the Gloster Meteor and de Havilland Vampire came too late to be of any use in the war. Therefore, they simply had no opportunity to gain iconic status.

Now, there's a book called Hurricane: Victor of the Battle of Britain by Leo McKinstry^[1] which argues much of the point you made in the question: that it was indeed the Hawker aeroplane which should have become the symbol of the RAF and its triumph over the Luftwaffe. His argument is that the Hurricane accounted for a significantly larger number of kills than the Spitfire during the Battle of Britain (but then again, they did make up the bulk of Fighter Command inventory^[2] ) and therefore, purely on combat merit, it should have been given more recognition.

The answer to the question why this did not happen is complex and, at least to a degree, need to be speculative.

Roland Beamont, one of Britain's most exquisite test pilots, wrote of the Hurricane and Spitfire:

In the spring and summer of 1940, although without the elegance and high altitude performance of the Spitfire, the Hurricane was a machine of its time and many of us would not have changed it for any other mount. We knew it as a rugged, stable, forgiving aeroplane which was tolerant of our clumsiness and the worst that the weather could do. It absorbed legendary amounts of enemy fire and kept flying . . . The Hurricane and the Spitfire made a great team, but I never regretted my posting to a Hurricane squadron in that fateful time.^[3]

This already gives us part of the answer we're looking for. The Hurricane was a rugged workhorse, an indispensable asset for the RAF. However, as is often the case with workhorses, they tend to be ovderlooked in favor of more glamorous aircraft. And glamorous the Spitfire was. I would therefore posit that one of the reasons why the Spitfire was held in higher regard was its sex appeal. Now, don't laugh. Beauty might be in the eyes of the beholder, but it’s an objective fact that the Spitfire airframe is sleeker and more pleasing aesthetically than its counterpart.

Moreover, the Spitfire had a feel of a flying race car rather than a combat machine.

The responsiveness . . . gave meaning to the cliche that you didn't fly a Spitfire at all; you wore it. Or, as Diana Barnato put it: ‘You moved, it moved.’ . . . The Spitfire was nose-heavy on the ground and would tip forward if braked harshly, but it was perfectly balanced in flight.^[4]

The Hurricane, on the other hand, was a gun plaform more than anything and was much more forgiving to a rookie pilot (some even called it an ‘idiot’s plane’ – favorably so).

The plane might not be as beautiful as the Spitfire, but, [the supporters of the Hurricane] say, it had better visibility, could be produced and maintained more easily, had a tighter turning circle, and could be landed with less difficulty because it had a wider undercarriage . . . Above all, it has been argued that the Hurricane was a better combat fighter because its thicker, straighter wings made it a more stable base for firing. On the Spitfire, the recoil from the Browning guns could suddenly knock almost 25 mph off the flying speed and lower the nose as if the landing flaps had been extended.^[5]

Thus, we come to our second conclusion: the Spitfire required significantly more skill to fly well. While it might seem to be a disadvantage from the perspective of an average pilot, if you were good, you could really do wonders in the cockpit of a Spit. I would speculate that if you were a Spitfire ace, you had a certain air of artistry about you. And Spitfire aces who had to ‘downgrade’ to the Hurricane didn’t really appreciate it:

After the Spit, she [the Hurricane] was like a flying brick –– a great, lumbering farmyard stallion compared with a dainty and gentle thoroughbred.

That was by Robert Stanford-Tuck.^[6]

All in all, the Spitfire had everything you’d expect of an icon: it was beautiful, sexy, tantalizing, and lethal. It was everything that the Hurricane was not (save for the lethality). But most importantly, it was also a better fighter all around, and in the long run had a lot more potential for upgrades. It’s not that the Spitfire didn’t deserve its iconic status, because it it did. The Hurricane, however, was apparently not glamorous enough to achieve this status, even though its performance during the Battle of Britain would have warranted it.

Sources:

Roland Beamont, Fighter Test Pilot. Book Club Associates, 1986.

Leo McKinstry, Spitfire: Portrait of a Legend. John Murray, 2007.

Gilles Whittell, Spitfire Women of World War II. Harper Perennial, 2008.

Notes:

[1] I can't really provide you with McKinstry's entire book, but if you want, you can read this article in which the author summarizes his views on the Hurricane and Spitfire.

[2] McKinstry, p. 118.

[3] Beamont, p. 17.

[4] Whittell, p. 116.

[5] McKinstry, p. 115.

[6] McKinstry, p. 118.

The Spitfire was more iconic than many of the other British aircraft (note aircraft, not jets, the only WWII jet aircraft that were truly operated/produced by the UK were Gloster jets that were made in relatively small numbers), for a few reasons which I will attempt to break down for you.

Foremost, the Submarine Spitfire in its many variants was objectively a great fighter aircraft for the time period. In a number of metrics such as acceleration, rate of roll, climb, operational ceiling, and more the Spitfire performed exceptionally well (for a decent comparison by WWII ace Sqdn. Ldr. T.S. Wade, check out http://www.spitfireperformance.com/spittest.html) you can also find a whole website dedicated to Spitfire performance metrics here http://www.spitfireperformance.com/spittest.html . As the Spitfire was more agile, quicker, and quite simply better preferred by RAF pilots for dog-fighting, it was the logical choice for engaging German fighters like the Bf 109 which were, like the Spitfire, high performance and extremely effective planes. So in short Spitfires took much of the glory when it came to flashy dogfights, leaving some of the less flashy, but no less important work of patrols and bomber engagement to aircraft like the Hurricane.

Now aside from the performance advantages the Spitfire had, there too were cultural reasons the Spitfire ended up being considered more "iconic." Many places across the U.K. held "Spitfire Funds" where people were encouraged to donate to help build Spitfires, much of this effort was coordinated by newspapers and local organizations. In fact many large towns and corporations donated incredibly large sums of money and could proudly say that an R.A.F. Spitfire was flying with their name on it. More to the cultural reasons that the Spitfire ended up as much more possible is that there were a slew of World War II films in the 1960s that featured the Spitfire, (Reach For The Sky is the one that most comes to mind for me) and made it very recognizable for a post-war audience. Still today the Spitfire remains a popular aircraft with the public, Prince Harry even took one out for some spins last year to raise awareness for his scholarship fund.

I hope this answers at least the basic elements of your question, and please keep in mind that there are an incredible number of things that go into making something "iconic" and my answer only touches on the most basic of these for the Spitfire. For more information I highly recommend the Imperial War Museum for more info on the Spitfire and its history!