Marc P. answered 07/28/19
Ivy League Grad to Help with Standardized Tests and Academic Work
I'm unaware of any "exhaustive" collection, but you may want to consult the unicode character sets as well as ISO documentation (e.g., ISO/IEC 10646). Keep in mind:
1) For much of the history of the English language, very little was standardized. Scribes and printers would often use symbols imported from other languages or even of their own invention. Many symbols have been used over the years and eventually discarded, such as the long s, eth, and the "ae" and "oe" ligatures. Some may have been used locally or for only a short period of time.
2) Many symbols are used in English texts that are not strictly part of the English language, such as mathematical symbols and IPA pronunciation symbols.
3) If by "characters or symbols" you mean graphemes, then it might be possible to collect all. If you mean glyphs, then the challenge would be much greater.