Well, of course there have been English composers, and some of them are quite famous. Gustav Holst's "The Planets" is possibly one of the most famous pieces of classical music out there, and there are other hugely famous guys like Arthur Sullivan, Edwin Elgar, and Benjamin Britten.

But you are right that the England presence in classical music seems to be very diminished when we compare it to, say, Austria or Italy. Part of that is because music history stresses Austria and Germany a lot due in part to the fact that that's where music history as a discipline gets its real impetus, and Italy is the home of Catholicism, plus the Renaissance, then Opera, making it the hotbed of a lot of important musical developments. There's more discussion on these points here.

Another reason is that England really doesn't have its own indigenous resource for training classical musicians for the critical point during which the "canon" of classical music is cultivated (ie, the eighteenth and nineteenth centuries). The Royal College of Music, for instance, was only established in 1882. Meanwhile, Paris had their Conservatoire since 1795, and the Naples Conservatory has roots stretching back into the 17th century. And the kind of training cultivated in Neapolitan conservatories (which also inspired networks of training not affiliated with academia, such as Padre Martini in Bologna) was extremely powerful in shaping the lives of some of the century's greatest musicians, including Natives like Pergolesi and Rossini, as well as foreigners like Hasse, Haydn, and Mozart. In the Eighteenth Century, if you wanted to be a real composer, you went to Italy. (See Heartz, Music in European Capitals and Robinson, Naples and Neapolitan Opera).

Actually, the lack of sufficient training for a professional class of indigenous artists was a pretty big problem for some learned members of British society, whether musical or otherwise. All the best stars and the best positions seemed to go to continental musicians like Handel, JC Bach, and Haydn. The early history of the English Royal Academy (an arts institute, rather than a musical one) can nonetheless tell us something about the tensions surrounding arts education. Italian teachers were the ones who actually had the skill sets to train students, but they were continually shunned by their English colleagues, passed over for top positions, because they weren't indigenous. English literati desperately wanted to import the Italianate approach to artistic training to train indigenous artists, but they rebuked and disrespected the very teachers they brought in to help. For more details on efforts to establish arts education in England, see West, "Xenophobia and xenomania: Italians and the English Royal Academy" in Italian Culture in Northern Europe in the Eighteenth Century.

The oldest Conservatory in England is the Royal Academy of Music, established in 1820. This is contemporaneous with the development of a bunch of conservatories across Europe, but the Academy did not have good direction and not a lot of prestige (at least until the 1860s). In fact, Sullivan, possibly the greatest graduate of the Academy, actually split his time between the Academy and the Leipzig Conservatory. So they can't even claim full responsibility for him.

But once the Royal College of Music gets going in the 1880s, then England begins to gain a real foothold in the classical world. In fact, besides Sullivan, all the major English composers I named above are alumni of the Royal College. That should really tell you something about how essential an institution like that is for cultivating a real tradition of art music production in a country!