There are, or at least were (on loan words, mostly) until very recently. It is still not too uncommon to see words like naïve or coöperate, with a dieresis on the second of two letters indicating that it's a two-syllable pronunciation of the vowels (co-op-er-ate) and not a single glide or lengthening (coo-per-ate). The use of this particular diacritic has fallen out of style in most publications, though there are still some which have style guides requiring it. Of course you'll also sometimes find it in words that people still consider foreign despite their widespread use (café, résumé vs resume, façade). Façade is actually a good example of a word which no one would doubt is now English, but which is almost never spelled with the cedilla on the <c>. (Breaking the 20-year rule a second: Computers are also having a small part in this as many English typers wouldn't necessarily know how to type <é>, even if they did care to do so).

Still, the real reason why they're not used is simply because they never saw widespread adoption. Remember that the English alphabet is really the Latin alphabet with some minor modification. Throughout the various efforts at spelling reforms, diacritics were never really introduced to the system being reformed. Instead, adjustments were made through the use of digraphs. For example we use <sh> for /ʃ/ instead of <š> or <ś>; We use <ni> in English for /ɲ/ (e.g. "onion", cf. French <gn> in "oignon") instead of <ñ> as in Spanish; German <ü> and <ö> are rendered as <ue> and <oe> respectively.

The answer to why English generally doesn't use diacritics is as simple as the fact that English never adopted them in the first place. ( <-- tldr) This isn't really for any particular reason for this other than possible personal preference or habits of typesetters. It wasn't any particular conscious decision to not use them.

You could argue that not using diacritics was better for the typesetters anyway since they wouldn't need to worry about the extra letters (n and ñ would be different pieces) than if they just skip them entirely, and this may actually have had something to do with the choice as well. As you can probably imagine, a traditional typesetter's shop would look very different between England and China.

Anyway I hope that answers your question.

Also, as a side note for future reference, /r/linguistics will get you slightly more researched answers than AskLinguistics. A lot of the answers in AskLinguistics tend to be more speculative or incomplete, or just overly superficial. Just something I've noticed recently. In this particular case your question is really about writing systems and not linguistics, so AskHistorians is probably the better place to be asking this one anyway.